Abstract
In this paper we prove refined major-balance identities on the $321$-avoiding involutions of length $n$, respecting the leading element of permutations. The proof is based on sign-reversing involutions on the lattice paths within a $\lfloor n/2 \rfloor \times \lceil n/2 \rceil$ rectangle. Moreover, we prove affirmatively a question about refined major-balance identities on the $123$-avoiding involutions, respecting the number of descents.
Citation
Tung-Shan Fu. Hsiang-Chun Hsu. Hsin-Chieh Liao. "Folding Phenomenon of Major-balance Identities on Restricted Involutions." Taiwanese J. Math. 22 (5) 1031 - 1050, October, 2018. https://doi.org/10.11650/tjm/180101
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