Related papers: A refined bijection between alternating permutatio…

Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…

We define a bijection between triangulations of a convex polygon and $312$-avoiding permutations through the process of "ear-clipping". This bijection is then used to obtain a bijection between polygon dissections and a certain class of…

A number of fields, including the study of genome rearrangements and the design of interconnection networks, deal with the connected problems of sorting permutations in "as few moves as possible", using a given set of allowed operations, or…

We present a simple a bijection between permutations of $\{1,..., n\}$ with $k$ descents and permutation tableaux of length $n$ with $k$ columns.

We initiate the study of sorting permutations using prefix block-interchanges, which exchange any prefix of a permutation with another non-intersecting interval. The goal is to transform a given permutation into the identity permutation…

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…

As a unification of increasing trees and plane trees, the weakly increasing trees labeled by a multiset was introduced by Lin-Ma-Ma-Zhou in 2021. Motived by some symmetries in plane trees proved recently by Dong, Du, Ji and Zhang, we…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

A well-known bijection between Motzkin paths and ordered trees with outdegree always $\le2$, is lifted to Grand Motzkin paths (the nonnegativity is dropped) and an ordered list of an odd number of such $\{0,1,2\}$ trees. This offers an…

Inspired by the definition of modified ascent sequences, we introduce a new class of integer sequences called revised ascent sequences. These sequences are defined as Cayley permutations where each entry is a leftmost occurrence if and only…

The in-order traversal provides a natural correspondence between binary trees with a decreasing vertex labeling and endofunctions on a finite set. By suitably restricting the vertex labeling we arrive at a class of trees that we call…

Higher dimensional permutations are tuples of d-1 permutations that can be identified with a point set in a d-dimensional grid. In N. Bonichon and P.-J. Morel, {\it J. Integer Sequences} 25 (2022), several conjectures regarding the…

Let $\pi=(\pi_1,\pi_2,\hdots,\pi_n)$ be permutation of the elements $1,2,\hdots,n. $ Positive integer $k\leq2^{n-1}$ we call index of $\pi,$ if in its binary notation as $n$-digital binary number, the 1's correspond to the ascent points. We…

We present a simplified variant of Biane's bijection between permutations and 3-colored Motzkin paths with weight that keeps track of the inversion number, excedance number and a statistic so-called depth of a permutation. This generalizes…

A bijection $\Phi$ is presented between plane bipolar orientations with prescribed numbers of vertices and faces, and non-intersecting triples of upright lattice paths with prescribed extremities. This yields a combinatorial proof of the…

We define a deterministic family of permutations generated by an alternating center-edge extraction process on the ordered set [n] = {1,2,...,n}. Starting from the ordered list (1,2,...,n), one repeatedly removes the median element or…

The purpose of this paper is twofold. First we answer to a question asked by Steingrimsson and Williams about certain permutation tableaux: we construct a bijection between binary trees and the so-called Catalan tableaux. These tableaux are…

We present a simple bijection between permutation matrices and descending plane partitions without special parts. This bijection is already mentioned in work of P. Lalonde (without giving the details); it involves the inversion words of…

Under what circumstances might every extension of a combinatorial structure contain more copies of another one than the original did? This property, which we call prolificity, holds universally in some cases (e.g., finite linear orders) and…

In this paper, we connect two types of representations of a permutation $\sigma$ of the finite field $\F_q$. One type is algebraic, in which the permutation is represented as the composition of degree-one polynomials and $k$ copies of…