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
For any r-order {0,1}-tensor A with e ones, we prove that the spectral radius of A is at most exp((r-1)/r) with the equality holds if and only if e=k^r for some integer k and all ones forms a principal sub-tensor 1_{k x k x ... x k}. We also prove a stability result for general tensor A with e ones where e = k^r+l with relatively small l. Using the stability result, we completely characterized the tensors achieving the maximum spectral radius among all r-order {0,1}-tensor A with k^r+l ones, for -r-1 ≤ l ≤ r, and k sufficiently large.
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@inproceedings{shuliang2018spectral,
  title={Spectral radius of {0,1}-tensor with prescribed number of ones},
  author={Shuliang Bai, and Liuyuan Lu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220318133146586129011},
  booktitle={Linear Algebra and its Applications},
  volume={558},
  pages={205-235},
  year={2018},
}
Shuliang Bai, and Liuyuan Lu. Spectral radius of {0,1}-tensor with prescribed number of ones. 2018. Vol. 558. In Linear Algebra and its Applications. pp.205-235. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220318133146586129011.
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