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arXiv · 1711.04601

Folding Phenomenon of Major-balance Identities on Restricted Involutions

Tung-Shan Fu·Hsian-Chun Hsu·Hsin-Chieh Liao
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Abstract

In this paper we prove a refined major-balance identity on the $321$-avoiding involutions of length $n$, respecting the leading element of permutations. The proof is based on a sign-reversing involution on the lattice paths within a $\lfloor\frac{n}{2}\rfloor\times\lceil\frac{n}{2}\rceil$ rectangle. Moreover, we prove affirmatively a question about refined major-balance identity on the $123$-avoiding involutions, respecting the number of descents.

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Tung-Shan Fu, Hsian-Chun Hsu, Hsin-Chieh Liao. 2017-11-13. Folding Phenomenon of Major-balance Identities on Restricted Involutions. https://arxiv.org/abs/1711.04601

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