Combinatorics

[1] Witten-Morse functions and Morse inequalities on digraphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Chong Wang School of Mathematics, Renmin University of China, Beijing 100872, China; School of Mathematics and Statistics, Cangzhou Normal University, 061000 China

Combinatorics Algebraic Topology and General Topology mathscidoc:2207.06006

arXiv, 2021.8
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[2] The adjoint braid arrangement as a combinatorial Lie algebra via the Steinmann relations

Zhengwei Liu William Norledge Adrian Ocneanu

Combinatorics mathscidoc:2207.06005

2022.1
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[3] Discrete Morse Theory on Digraphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Chong Wang School of Mathematics, Renmin University of China, Beijing 100872, China; School of Mathematics and Statistics, Cangzhou Normal University, 061000 China Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge MA 02138, USA

Combinatorics Algebraic Topology and General Topology mathscidoc:2207.06004

Pure and Applied Mathematics Quarterly
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[4] Calculus of variations on locally finite graphs

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Yunyan Yang Department of Mathematics, Renmin University of China, Beijing, 100872, China

Analysis of PDEs Combinatorics mathscidoc:2207.03009

Revista Matemática Complutense, 2021.9
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[5] A heat flow for the mean field equation on a finite graph

Yong Lin Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, People’s Republic of China Yunyan Yang Department of Mathematics, Renmin University of China, Beijing, 100872, People’s Republic of China

Analysis of PDEs Combinatorics mathscidoc:2207.03008

Calculus of Variations and Partial Differential Equations, 60, (206), 2021.8
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[6] Equivalent Properties for CD Inequalities on Graphs with Unbounded Laplacians

Chao Gong School of Information, Renmin University of China, Beijing 100872, China Yong Lin 1School of Information, Renmin University of China, Beijing 100872, China.

Combinatorics Differential Geometry mathscidoc:2207.06003

Chinese Annals of Mathematics, Series B, 38, 1059–1070, 2017.9
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[7] On-diagonal lower estimate of heat kernels on graphs

Yong Lin Department of Mathematics, Renmin University of China, Beijing 100872, PR China Yiting Wu Department of Mathematics, Renmin University of China, Beijing 100872, PR China

Analysis of PDEs Combinatorics mathscidoc:2207.03003

Journal of Mathematical Analysis and Applications, 456, (2), 1040-1048, 2017.12
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[8] Quantum tunneling on graphs

Yong Lin Department of Mathematics, Information School, Renmin University of China, Beijing, People’s Republic of China Gábor Lippner Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA Shing-Tung Yau Department of Mathematics, Harvard University, Cambridge, MA, 02138, USA

Combinatorics Mathematical Physics mathscidoc:2207.06002

Communications in Mathematical Physics, 311, 113–132, 2012.2
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[9] Ricci curvature of graphs

Yong Lin Renmin University, Department of Mathematics, Beijing 100872, China Linyuan Lu University of South Carolina, Department of Mathematics, Columbia, SC 29208, USA Shing-Tung Yau Harvard University, Department of Mathematics, Cambridge, MA 02138, USA

Combinatorics mathscidoc:2207.06001

Tohoku Mathematical Journal, 63, (4), 605-627, 2011.10
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[10] C-sortable words as green mutation sequences

Yu Qiu Institutt for Matematiske Fag, NTNU, 7491 Trondheim, Norway

Combinatorics mathscidoc:2206.06001

Proceedings of the London Mathematical Society, 111, (5), 1052-1070, 2015.11
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[11] Cluster combinatorics of d-cluster categories

Yu Zhou Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, PR China Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, PR China

Combinatorics Representation Theory mathscidoc:2204.06004

Journal of Algebra, 321, (10), 2898-2915, 2009.5
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[12] Cluster algebras arising from cluster tubes

Yu Zhou Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China, Current address:, Fakultät für Mathematik, Universität Bielefeld, D-33501, Bielefeld, Germany Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China, bzhu@math.tsinghua.edu.cn

Combinatorics Representation Theory Rings and Algebras mathscidoc:2204.06003

Journal of the London Mathematical Society, 89, (3), 703-723, 2014.6
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[13] Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization

Yu Zhou Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

Combinatorics Representation Theory Rings and Algebras mathscidoc:2204.06002

Algebra and Representation Theory, 21, 817-832, 2017.10
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[14] Cotorsion pairs in cluster categories of type A^\infty_\infty

Huimin Chang Department of Applied Mathematics, School of Education, The Open University of China, 100039 Beijing, China Yu Zhou Yau Mathematical Sciences Center, Tsinghua University, 100084 Beijing, China Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, China

Combinatorics Representation Theory mathscidoc:2204.06001

Journal of Combinatorial Theory, Series A, 156, 119-141, 2018.5
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[15] Spectral radius of {0,1}-tensor with prescribed number of ones

Shuliang Bai University of South Carolina, Columbia, SC 29208, United States of America Liuyuan Lu University of South Carolina, Columbia, SC 29208, United States of America

Combinatorics mathscidoc:2203.06005

Linear Algebra and its Applications, 558, 205-235, 2018.12
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[16] Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature

D. Cushing Department of Mathematical Sciences, Durham University, United Kingdom of Great Britain and Northern Ireland S. Kamtue Department of Mathematical Sciences, Durham University, United Kingdom of Great Britain and Northern Ireland J. Koolen School of Mathematical Sciences, University of Science and Technology of China, and Wu Wen-Tsun Key Laboratory of Mathematics of CAS, Hefei, China S. Liu School of Mathematical Sciences, University of Science and Technology of China, and Wu Wen-Tsun Key Laboratory of Mathematics of CAS, Hefei, China F. Münch nstitute of Mathematics, Universität Potsdam, Germany N. Peyerimhoff Department of Mathematical Sciences, Durham University, United Kingdom of Great Britain and Northern Ireland

Combinatorics Differential Geometry mathscidoc:2203.06004

Advances in Mathematics, 369, 107188, 2020.8
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[17] The set of vertices with positive curvature in a planar graph with nonnegative curvature

Bobo Hua School of Mathematical Sciences, LMNS, Fudan University, Shanghai 200433, China; Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, China Yanhui Su College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China

Combinatorics Differential Geometry mathscidoc:2203.06003

Advances in Mathematics, 343, 789-820, 2019.2
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[18] Equiangular lines with a fixed angle

Zilin Jiang Arizona State University, Tempe AZ 85287 Jonathan Tidor Massachusetts Institute of Technology, Cambridge MA 02141 Yuan Yao Massachusetts Institute of Technology, Cambridge MA 02141 Shengtong Zhang Massachusetts Institute of Technology, Cambridge MA 02141 Yufei Zhao Massachusetts Institute of Technology, Cambridge MA 02141

Combinatorics Metric Geometry mathscidoc:2203.06002

Annals of Mathematics, 194, (3), 729-743, 2021.1
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[19] Small cancellation labellings of some infinite graphs and applications

Damian Osajda Instytut Matematyczny, Uniwersytet Wrocławski, Wrocław, Poland; and Fakultät für Mathematik, Universität Wien, Austria

Combinatorics Functional Analysis Group Theory and Lie Theory mathscidoc:2203.06001

Acta Mathematica, 225, (1), 159-191, 2020.11
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[20] An old problem of Erd\H os: a graph without two cycles of the same length

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:2110.06001

arXiv:2110.04696, 2021.10
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[21] Some extremal problems on graph theory

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:2108.06001

The 22nd Conference of the International Federation of Operational Research Societies, 2021.8
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[22] The Kelmans-Seymour conjecture I: Special separations

Dawei He School of Mathematics, Georgia Institute of Technology, Atlanta Yan Wang School of Mathematics, Georgia Institute of Technology, Atlanta Xingxing Yu School of Mathematics, Georgia Institute of Technology, Atlanta

Combinatorics mathscidoc:2105.41004

2019.4
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[23] The Kelmans-Seymour conjecture III: 3-vertices in K− 4

Dawei He School of Mathematics, Georgia Institute of Technology, Atlanta Yan Wang School of Mathematics, Georgia Institute of Technology, Atlanta Xingxing Yu School of Mathematics, Georgia Institute of Technology, Atlanta

Combinatorics mathscidoc:2105.41003

2019.6
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[24] The Kelmans-Seymour conjecture IV: A proof

Dawei He School of Mathematics, Georgia Institute of Technology, Atlanta Yan Wang School of Mathematics, Georgia Institute of Technology, Atlanta Xingxing Yu School of Mathematics, Georgia Institute of Technology, Atlanta

Combinatorics mathscidoc:2105.41002

2019.5
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[25] The Kelmans-Seymour conjecture II: 2-Vertices in K− 4

Dawei He School of Mathematics, Georgia Institute of Technology, Atlanta Yan Wang School of Mathematics, Georgia Institute of Technology, Atlanta Xingxing Yu School of Mathematics, Georgia Institute of Technology, Atlanta

Combinatorics mathscidoc:2105.41001

2019.8
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[26] Representations of mock theta functions

Dandan Chen East China Normal University Liuquan Wang Wuhan University

Classical Analysis and ODEs Combinatorics Number Theory mathscidoc:2103.05001

Advances in Mathematics, 365, 107037, 2020
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[27] Zeros of the deformed exponential function

Liuquan Wang Wuhan University Cheng Zhang Johns Hopkins University

Analysis of PDEs Classical Analysis and ODEs Combinatorics Number Theory mathscidoc:2103.03003

Advances in Mathematics, 332, 311–348, 2018
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[28] Persistent spectral graph

Rui Wang Michigan State University Duc Duy Nguyen University of Kentucky Guowei Wei Michigan State University

Combinatorics Data Analysis, Bio-Statistics, Bio-Mathematics Algebraic Topology and General Topology mathscidoc:2103.06001

Int J Numer Meth Biomed Engng, 36, 2020.4
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[29] Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture

Hao Huang Emory University

Combinatorics Information Theory mathscidoc:2005.06001

Best Paper Award in Applied Mathematics in 2020

Annals of Mathematics, 190, 949-955, 2019.11
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[30] Pretty good state transfer in graphs with an involution

Mark Kempton Gabor Lippner Shing-Tung Yau

Combinatorics mathscidoc:1912.43701

arXiv preprint arXiv:1702.07000, 2017.2
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[31] Ricci-flat cubic graphs with girth five

David Cushing Riikka Kangaslampi Yong Lin Shiping Liu Linyuan Lu Shing-Tung Yau

Combinatorics mathscidoc:1912.43700

arXiv preprint arXiv:1802.02982, 2018.2
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[32] Erratum for Ricci-flat graphs with girth at least five

David Cushing Riikka Kangaslampi Yong Lin Shiping Liu Linyuan Lu Shing-Tung Yau

Combinatorics mathscidoc:1912.43688

arXiv preprint arXiv:1802.02979, 2018.2
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[33] Relationships between cycle spaces, gain graphs, graph coverings, fundamental groups, path homology, and graph curvature

Mark Kempton Florentin Munch Shing-Tung Yau

Combinatorics mathscidoc:1912.43671

arXiv preprint arXiv:1710.01264, 2017.10
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[34] Spanning trees in subgraphs of lattices

Shing-Tung Yau ST Yau

Combinatorics mathscidoc:1912.43640

Contemporary Mathematics, 245, 201-220, 1999
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[35] Discrete Greens functions and random walks on graphs

Hao Xu Shing-Tung Yau

Combinatorics mathscidoc:1912.43629

Journal of Combinatorial Theory, Series A, 120, (2), 483-499, 2013.2
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[36] Sharp DaviesGaffneyGrigoryan lemma on graphs

Frank Bauer Bobo Hua Shing-Tung Yau

Combinatorics mathscidoc:1912.43621

Mathematische Annalen, 368, 1429-1437, 2017.8
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[37] A Harnack inequality for Dirichlet eigenvalues

Shing-Tung Yau ST Yau

Combinatorics mathscidoc:1912.43604

Journal of Graph Theory, 34, (4), 247-257, 2000.8
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[38] Eigenvalues of graphs and Sobolev inequalities

Fan RK Chung Shing-Tung Yau

Combinatorics mathscidoc:1912.43533

Combinatorics, Probability and Computing, 4, (1), 11-25, 1995.3
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[39] Coverings, heat kernels and spanning trees

Fan Chung Shing-Tung Yau

Combinatorics mathscidoc:1912.43510

Journal of Combinatorics, 6, 163-184
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[40] Laplacian simplices associated to digraphs

Gabriele Balletti Stockholm University Takayuki Hibi Osaka University Marie Meyer University of Kentucky Akiyoshi Tsuchiya Osaka University

Combinatorics mathscidoc:1912.43014

Arkiv for Matematik, 56, (2), 243 – 264, 2018
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[41] Counterexamples to Strassen’s direct sum conjecture

Yaroslav Shitov Moscow, Russia

Combinatorics mathscidoc:1911.43033

Acta Mathematica, 222, (2), 363 – 379, 2017
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[42] Spectral theory of infinite quantum graphs

Pavel Exner Aleksey Kostenko Mark Malamud Hagen Neidhardt

Combinatorics mathscidoc:1910.43179

Annales Henri Poincar, 19, (11), 3457-3510, 2018.11
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[43] On the finiteness of quantum K-theory of a homogeneous space

David Anderson Ohio State University Linda Chen Swarthmore College Hsian-Hua Tseng Ohio State University

Combinatorics Representation Theory mathscidoc:1907.01005

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[44] On the number of edges in some graphs

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:1905.06001

Discrete Applied Mathematics (2020), https://doi.org/10.1016/j.dam.2020.03.008 , 283, 751–755, 2020.3
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[45] An Lp theory of sparse graph convergence I: limits, sparse random graph models, and power law distributions

Christian Borgs Microsoft Research Jennifer T. Chayes Microsoft Research Henry Cohn Microsoft Research Yufei Zhao MIT

Combinatorics Probability mathscidoc:1904.06003

Transactions of the American Mathematical Society
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[46] Upper tails and independence polynomials in random graphs

Bhaswar B. Bhattacharya University of Pennsylvania Shirshendu Ganguly UC Berkeley Eyal Lubetzky New York University Yufei Zhao MIT

Combinatorics Probability mathscidoc:1904.06002

Advances in Mathematics, 319, 313-347, 2017
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[47] A relative Szemerédi theorem

David Conlon Oxford Jacob Fox Stanford Yufei Zhao MIT

Combinatorics Number Theory mathscidoc:1904.06001

Geometric and Functional Analysis , 25, 733-762, 2015
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[48] On regularity lemmas and their algorithmic applications

Jacob Fox Stanford László Miklós Lovász MIT Yufei Zhao MIT

Combinatorics mathscidoc:1811.06001

Distinguished Paper Award in 2018

Combinatorics, Probability and Computing, 26, (4), 481-505, 2017.7
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[49] Detecting topology change via correlations and entanglement from gauge/gravity correspondence

Hai Lin Tsinghua University Keyou Zeng Tsinghua University

Combinatorics Mathematical Physics mathscidoc:1804.06009

J.Math.Phys., 59, (3), 032301, 2018.3
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[50] On the Newton polyhedrons with one inner lattice point

Xue Luo Beihang University Fang Wang Beihang University

Combinatorics mathscidoc:1804.06008

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[51] Large induced forests in graphs

Lingsheng Shi Tsinghua Hongyu Xu Tsinghua

Combinatorics mathscidoc:1804.06007

2017
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[52] Curvature aspects of graphs

F. BAUER Max Planck Institute for Mathematics in the Sciences F. CHUNG University of California, San Diego Yong Lin Renmin University of China Yuan Liu Institute of Computational Mathematics and Scientific/Engineering Computing. Chinese Academy of Sciences

Combinatorics Geometric Analysis and Geometric Topology mathscidoc:1804.06006

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 145, 2033-2042, 2017.1
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[53] The existence and nonexistence of global solutions for a semilinear heat equation on graphs

Yong Lin Renmin University of China Yiting Wu Renmin University of China

Analysis of PDEs Combinatorics mathscidoc:1804.03003

Calculus of Variations and Partial Differential Equations, 56, 2017.3
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[54] Stochastic completeness for graphs with curvature dimension conditions

Bobo Hua Fudan University Yong Lin Renmin University of China

Combinatorics Geometric Analysis and Geometric Topology mathscidoc:1804.06005

Advances in Mathematics, 306, 279-302, 2017.1
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[55] Kazdan–Warner equation on graph

Alexander Grigor’yan University of Bielefeld Yong Lin Renmin University of China Yunyan Yang Renmin University of China

Analysis of PDEs Combinatorics mathscidoc:1804.03002

Calculus of Variations and Partial Differential Equations, 55, 2016.7
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[56] Yamabe type equations on graphs

Alexander Grigor’yan University of Bielefeld Yong Lin Renmin University of China Yunyan Yang Renmin University of China

Analysis of PDEs Combinatorics mathscidoc:1804.03001

Journal of Differential Equations, 261, 4924-4943, 2016.2
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[57] Cohomology of digraphs and (undirected) graphs

ALEXANDER GRIGOR’YAN University of Bielefeld Yong Lin Renmin University of China YURI MURANOV University of Warmia and Mazury Shing-Tung Yau Harvard University

Combinatorics mathscidoc:1804.02001

ASIAN JOURNAL OF MATHEMATICS, 887-932, 2015.9
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[58] Li-Yau inequality on graphs

Frank Bauer Harvard University Paul Horn University of Denver Yong Lin Renmin University of China Gabor Lippner Northeastern University Dan Mangoubi Hebrew University Shing-Tung Yau Harvard University

Combinatorics Differential Geometry mathscidoc:1804.06004

Journal of differential geometry, 99, 359-405, 2015.6
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[59] Ricci-flat graphs with girth at least five

Yong Lin Renmin University of China Linyuan Lu University of South Carolina S.-T. Yau Harvard University

Combinatorics mathscidoc:1804.06003

communications in analysis and geometry, 22, 1-17, 2014.7
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[60] Harnack inequalities for graphs with non-negative Ricci curvature

Fan Chung University of California, SanDiego Yong Lin Renmin University o China S.-T. Yau Harvard University

Combinatorics Geometric Analysis and Geometric Topology mathscidoc:1804.06002

Journal of Mathematical Analysis and Applications, 415, 25-32, 2014.1
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[61] Homotopy Theory for Digraphs

Alexander Grigor’yan University of Bielefeld Yong Lin Renmin University of China Yuri Muranov University of Warmia and Mazury Shing-Tung Yau Harvard University

Combinatorics mathscidoc:1804.06001

Pure and Applied Mathematics Quarterly, 10, 619-674, 2014
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[62] Enumeration of points, lines, planes, etc.

June Huh Institute for Advanced Study Botong Wang University of Wisconsin-Madison

Combinatorics Convex and Discrete Geometry mathscidoc:1803.43005

Acta Mathematica, 218, (2), 2017
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[63] On the size of graphs without repeated cycle lengths

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:1711.06001

Discrete Applied Mathematics, 232, 226-229, 2017.12
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[64] Koszulity of directed categories in representation stability theory

Wee Liang Gan Liping Li

Combinatorics K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1702.06003

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[65] Noetherian property of infinite EI categories

Wee Liang Gan Liping Li

Combinatorics Representation Theory Rings and Algebras mathscidoc:1702.06002

New York J. Math., 21, 369-382, 2015
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[66] Graphs without repeated cycle lengths

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:1702.06001

Australasian Journal of Combinatorics, 27, 101-105, 2003.3
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[67] Noise correlation bounds for uniform low degree functions

Per Austrin Department of Computer Science, University of Toronto Elchanan Mossel University of California, Berkeley, 367 Evans Hall, Berkeley, CA, U.S.A.

Combinatorics Optimization and Control mathscidoc:1701.06003

Arkiv for Matematik, 51, (1), 29-52, 2010.8
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[68] Some combinatorial properties of flag simplicial pseudomanifolds and spheres

Christos A. Athanasiadis Department of Mathematics, University of Athens

Combinatorics Convex and Discrete Geometry mathscidoc:1701.06002

Arkiv for Matematik, 49, (1), 17-29, 2009.4
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[69] On the generalized lower bound conjecture for polytopes and spheres

Satoshi Murai Department of Mathematical Science, Faculty of Science, Yamaguchi University Eran Nevo Department of Mathematics, Ben Gurion University of the Negev

Combinatorics Arithmetic Geometry and Commutative Algebra mathscidoc:1701.06001

Acta Mathematica, 210, (1), 185-202, 2012.4
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[70] Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve

Jean Bourgain School of Mathematics, Institute for Advanced Study Alex Gamburd Department of Mathematics, University of California at Santa Cruz Peter Sarnak School of Mathematics, Institute for Advanced Study

Analysis of PDEs Combinatorics Functional Analysis mathscidoc:1701.03005

Acta Mathematica, 207, (2), 255-290, 2009.12
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[71] Potentially $K_{m}-G$-graphical Sequences: A Survey

Lai Chunhui Minnan Normal University Hu Lili Minnan Normal University

Combinatorics mathscidoc:1612.06004

Czechoslovak Mathematical Journal, 59, 1059-1075, 2009.12
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[72] A Lower Bound for the Number of Edges in a Graph Containing No Two Cycles of the Same Length

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:1612.06003

Electronic Journal of Combinatorics, 8, 2001.10
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[73] On the size of graphs with all cycle having distinct length

Lai Chunhui Minnan Normal University

Combinatorics mathscidoc:1612.06002

Discrete Mathematics, 122, 363-364, 1993.12
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[74] Some open problems on cycles

Lai Chunhui Minnan Normal University Liu Mingjing Minnan Normal University

Combinatorics mathscidoc:1612.06001

Journal of Combinatorial Mathematics and Combinatorial Computing, 91, 51-64, 2014.11
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[75] Chemical indices, mean distance, and radius

Lingsheng Shi Tsinghua University

Combinatorics mathscidoc:1611.06003

MATCH Communications in Mathematical and in Computer Chemistry, 75, 57-70, 2016
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[76] On Turán densities of small triple graphs

Lingsheng Shi Tsinghua University

Combinatorics mathscidoc:1611.06002

European Journal of Combinatorics, 52, 95-102, 2016
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[77] Trees with given maximum degree minimizing the spectral radius

Xu Du Beijing Jiaotong University Lingsheng Shi Tsinghua University

Combinatorics mathscidoc:1611.06001

Electronic Journal of Linear Algebra, 31, 335-361, 2016
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[78] Rank n swapping algebra for the PSL(n;R) Hitchin component

Zhe Sun Yau Mathematical Sciences Center

Combinatorics Differential Geometry mathscidoc:1609.06001

International Mathematics Research Notices, 2017, (2), 583-613, 2017.2
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[79] Volume doubling, Poincar\'{e} inequality and Gaussian heat kernel estimate for non-negatively curved graphs

Paul Horn Denver University Yong Lin Renmin University of China Shuang Liu Renmin University of China Shing-Tung Yau Harvard University

Combinatorics Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1608.10074

Journal für die reine und angewandte Mathematik, 2017.12
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