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arXiv · 1808.05736

Combinatorial identities related to $2\times 2$ submatrices of recursive matrices

Fangfang Cai·Qing-Hu Hou·Yidong Sun·Arthur L. B. Yang
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Abstract

Recursive matrices are ubiquitous in combinatorics, which have been extensively studied. We focus on the study of the sums of $2\times 2$ minors of certain recursive matrices, the alternating sums of their $2\times 2$ minors, and the sums of their $2\times 2$ permanents. We obtain some combinatorial identities related to these sums, which generalized the work of Sun and Ma in [{\it Electron. J. Combin. 2014}] and [{\it European J. Combin. 2014}]. With the help of the computer algebra package {\tt HolonomicFunctions}, we further get some new identities involving Narayana polynomials.

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Fangfang Cai, Qing-Hu Hou, Yidong Sun, Arthur L. B. Yang. 2018-08-17. Combinatorial identities related to $2\times 2$ submatrices of recursive matrices. https://arxiv.org/abs/1808.05736

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