We give a Pieri rule for the torus-equivariant cohomology of (submaximal) Grassmannians of Lie types B, C, and D. To the authors' best knowledge, our rule is the rst manifestly positive formula, beyond the equivariant Chevalley formula. We also give a simple proof of the equivariant Pieri rule for the ordinary (type A) Grassmannian.

In this paper, we show that general homogeneous manifolds G/P satisfy Conjecture O of Galkin, Golyshev and Iritani which `underlies' Gamma conjectures I and II of them. Our main tools are the quantum Chevalley formula for G/P and a theory on nonnegative matrices including Perron-Frobenius theorem.

entangled states. We construct sets of fewer than d orthogonal maximally entangled states which are not distinguished by one-way local operations and classical communication (LOCC) in the Hilbert space of d ⊗ d. The proof, based on the Fourier transform of an additive group, is very simple but quite effective. Simultaneously, our results give a general unified upper bound for the minimum number of one-way LOCC indistinguishable maximally entangled states. This improves previous results which only showed sets of N  d − 2 such states. Finally, our results also show that previous conjectures in Zhang et al. [Z.-C. Zhang, Q.-Y. Wen, F. Gao, G.-J. Tian, and T.-Q. Cao, Quant. Info. Proc. 13, 795 (2014)] are indeed correct.

Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three nonzeros. Recently, the authors of [37]constructed a class of cyclic codes with arbitrary number of nonzeros, and computed the weight distribution for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by introducing certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.

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