格路与避免模式的有唯一排序的排列

使用避免Vincular模式的栈进行栈排序

Stack-sorting with Stacks Avoiding Vincular Patterns

本文提出一种通过避免Vincular模式的栈进行右贪心排序的新映射，统一了已有经典与连续避免模式的栈排序框架，并对多个长度3模式刻画了排序类、原像最大规模和周期点。

关于避免(132,213)的循环排列增长率的一个下界

A lower bound on the growth rate of $(132,213)$-avoiding cyclic permutations

研究给出避免(132,213)的循环排列增长率的首个非平凡下界。构建新约简过程，迭代可判断是否为循环排列，反向能构建此类排列。还得出奇偶大小类双射及受限层数排列精确计数等结果。

Weak ascent sequences and related combinatorial structures

In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular length-4 bivincular pattern; upper-triangular binary matrices that satisfy a column-adjacency rule; factorial posets that are weakly (3+1)-free. We also show how weak ascent sequences are related to a class of pattern avoiding inversion sequences that has been a topic of recent research by Auli and Elizalde. Finally, we consider the problem of enumerating these n…

Decompositions and statistics for beta(1,0)-trees and nonseparable permutations

The subject of pattern avoiding permutations has its roots in computer science, namely in the problem of sorting a permutation through a stack. A formula for the number of permutations of length n that can be sorted by passing it twice through a stack (where the letters on the stack have to be in increasing order) was conjectured by West, and later proved by Zeilberger. Goulden and West found a bijection from such permutations to nonseparable planar maps, and later, Jacquard and Schaeffer presented a bijection from these planar maps to certain labeled plane trees, called beta(1,0)-trees. Using…

Stack sorting with restricted stacks

The (classical) problem of characterizing and enumerating permutations that can be sorted using two stacks connected in series is still largely open. In the present paper we address a related problem, in which we impose restrictions both on the procedure and on the stacks. More precisely, we consider a greedy algorithm where we perform the rightmost legal operation (here "rightmost" refers to the usual representation of stack sorting problems). Moreover, the first stack is required to be $σ$-avoiding, for some permutation $σ$, meaning that, at each step, the elements maintained in the stack av…

通过禁止乘积模式的0-1矩阵排序避免模式的排列

Sorting Pattern-Avoiding Permutations via 0-1 Matrices Forbidding Product Patterns

本文通过禁止乘积模式的0-1矩阵理论，给出了避免排列模式排序问题中极值函数的几乎紧上下界，并证明无π序列排序可在O(n2^{(1+o(1))α(n)})时间内完成。

Mesh patterns and the expansion of permutation statistics as sums of permutation patterns

Any permutation statistic $f:\sym\to\CC$ may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: $f= Σ_τλ_f(τ)τ$. To provide explicit expansions for certain statistics, we introduce a new type of permutation patterns that we call mesh patterns. Intuitively, an occurrence of the mesh pattern $p=(π,R)$ is an occurrence of the permutation pattern $π$ with additional restrictions specified by $R$ on the relative position of the entries of the occurrence. We show that, for any mesh pattern $p=(π,R)$, we have $λ_p(τ) = (-1)^{|τ|-|π|}p^{\star}(τ)$ …