Joint distributions of statistics over permutations avoiding two patterns of length 3

Han, Tian and Kitaev, Sergey (2024) Joint distributions of statistics over permutations avoiding two patterns of length 3. Discrete Mathematics and Theoretical Computer Science. ISSN 1365-8050 (In Press)

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Abstract

Finding distributions of permutation statistics over pattern-avoiding classes of permutations attracted much attention in the literature. In particular, Bukata et al.~¥cite{Bukata2019} found distributions of ascents and descents on permutations avoiding any two patterns of length 3. In this paper, we generalize these results in two different ways: we find explicit formulas for the joint distribution of six statistics ($¥asc$, $¥des$, $¥lrmax$, $¥lrmin$, $¥rlmax$, $¥rlmin$), and also explicit formulas for the joint distribution of four statistics ($¥asc$, $¥des$, $¥MNA$, $¥MND$) on these permutations in all cases. The latter result also extends the recent studies by Kitaev and Zhang~¥cite{KitZha} of the statistics $¥MNA$ and $¥MND$ (related to non-overlapping occurrences of ascents and descents) on stack-sortable permutations. All multivariate generating functions in our paper are rational, and we provide combinatorial proofs of five equidistribution results that can be derived from the generating functions.

ORCID iDs

Han, Tian and Kitaev, Sergey ORCID logoORCID: https://orcid.org/0000-0003-3324-1647;
CORE (COnnecting REpositories)