Abstract:In this paper, we find distribution of descents over $(n-3)$- and $(n-4)$-stack-sortable permutations in terms of Eulerian polynomials. Our results generalize the enumeration results by Claesson, Dukes, and Steingr\'ımsson on $(n-3)$- and $(n-4)$-stack-sortable permutations. Moreover, we find distribution of descents on $(n-2)$-, $(n-3)$- and $(n-4)$-stack-sortable permutations that avoid any given pattern of length 3, which extends known results in the literature on distribution of descents over pattern-avoiding 1- and 2-stack-sortable permutations. Our distribution results also give enumeration of $(n-2)$-, $(n-3)$- and $(n-4)$-stack-sortable permutations avoiding any pattern of length 3. One of our conjectures links our work to stack-sorting with restricted stacks, and the other conjecture states that 213-avoiding permutations sortable with $t$ stacks are equinumerous with 321-avoiding permutations sortable with $t$ stacks for any $t$.
From: Philip B. Zhang [view email]
[v1]
Fri, 28 Mar 2025 01:17:18 UTC (20 KB)
[v2]
Sun, 6 Apr 2025 02:06:39 UTC (19 KB)
[v3]
Sun, 13 Sep 2026 05:36:30 UTC (20 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。