Related papers: Equidistributed statistics on Fishburn matrices an…

In this paper, we study classes of subexcedant functions enumerated by the Bell numbers and present bijections on set partitions. We present a set of permutations whose transposition arrays are the restricted growth functions, thus defining…

We present an involution on set partitions that interchanges two statistics related to relative size of block entries and use it to establish an equidistribution on objects counted by the Bessel numbers.

Hypermaps were introduced as an algebraic tool for the representation of embeddings of graphs on an orientable surface. Recently a bijection was given between hypermaps and indecomposable permutations; this sheds new light on the subject by…

Ascent sequences were introduced by Bousquet-M\'elou, Claesson, Dukes and Kitaev, and are in bijection with unlabeled $(2+2)$-free posets, Fishburn matrices, permutations avoiding a bivincular pattern of length $3$, and Stoimenow matchings.…

Let $st=\{st_1,\ldots,st_k\}$ be a set of $k$ statistics on permutations with $k\geq 1$. We say that two given subset of permutations $T$ and $T'$ are $st$-Wilf-equivalent if the joint distributions of all statistics in $st$ over the sets…

A notable problem within permutation patterns that has attracted considerable attention in literature since 1973 is the search for a bijective proof demonstrating that 123-avoiding and 132-avoiding permutations are equinumerous, both…

A bijection is presented between (1): partitions with conditions $f_j+f_{j+1}\leq k-1$ and $ f_1\leq i-1$, where $f_j$ is the frequency of the part $j$ in the partition, and (2): sets of $k-1$ ordered partitions $(n^{(1)}, n^{(2)}, ...,…

In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal…

In an award-winning expository article, V. Pozdnyakov and J.M. Steele gave a beautiful demonstration of the ramifications of a basic bijection for permutations. The aim of this note is to connect this correspondence to a seemingly unrelated…

We present a simple bijection between Baxter permutations of size $n$ and plane bipolar orientations with n edges. This bijection translates several classical parameters of permutations (number of ascents, right-to-left maxima,…

On the set of permutations of a finite set, we construct a bijection which maps the 3-vector of statistics $(maj-exc,des,exc)$ to a 3-vector $(maj\_2,\widetilde{des\_2},inv\_2)$ associated with the $q$-Eulerian polynomials introduced by…

Let $\ell,k$ be fixed positive integers. In an earlier work, the first and third authors established a bijection between $\ell$-cores with first part equal to $k$ and $(\ell-1)$-cores with first part less than or equal to $k$. This paper…

In a paper by Lin an interesting family of semipermutations comes out to index the elements of a cohomology basis of a Hessenberg type variety. The corresponding Betti numbers are a generalization of Eulerian numbers. We show three…

We construct a direct natural bijection between descending plane partitions without any special part and permutations. The directness is in the sense that the bijection avoids any reference to nonintersecting lattice paths. The advantage of…

We give an account on what is known on the subject of permutation matchings, which are bijections of a finite regular semigroup that map each element to one of its inverses. This includes partial solutions to some open questions, including…

We define a map between the set of permutations that avoid either the four patterns $3214,3241,4213,4231$ or $3124,3142,4123,4132$, and the set of Dyck prefixes. This map, when restricted to either of the two classes, turns out to be a…

We introduce a statistic $\pmaj$ on partitions of $[n]=\{1,2,..., n\}$, and show that it is equidistributed with the number of 2-crossings over partitions of $[n]$ with given sets of minimal block elements and maximal block elements. This…

We provide new Schmidt-type results through an investigation of two bijections, which are results involving partitions with parts counted only at given indices. Mork's bijection, the first of these, was originally given as a proof of…

Let $T_n$ be the set of 321-avoiding permutations of order $n$. Two properties of $T_n$ are proved: (1) The {\em last descent} and {\em last index minus one} statistics are equidistributed over $T_n$, and also over subsets of permutations…

Theorems relating permutations with objects in other fields of mathematics are often stated in terms of avoided patterns. Examples include various classes of Schubert varieties from algebraic geometry (Billey and Abe 2013), commuting…