DeepAI AI Chat

A Bijection Between Weighted Dyck Paths and 1234-avoiding Up-Down Permutations

11/30/2020

∙

by Justine Falque, et al.

∙

∙

Three-dimensional Catalan numbers are a variant of the classical (bidimensional) Catalan numbers, that count, among other interesting objects, the standard Young tableaux of shape (n,n,n). In this paper, we present a structural bijection between two three-dimensional Catalan objects: 1234-avoiding up-down permutations, and a class of weighted Dyck paths.

page 1

page 2

page 3

page 4

∙ 04/02/2021

Bijections from Dyck and Motzkin meanders with catastrophes to pattern avoiding Dyck paths

In this note, we present constructive bijections from Dyck and Motzkin m...

0 Jean-Luc Baril, et al. ∙

∙ 07/29/2021

Mesosome Avoidance

We consider avoiding mesosomes – that is, words of the form xx' with x' ...

0 Robert Cummings, et al. ∙

∙ 03/10/2019

Asymptotically faster algorithm for counting self-avoiding walks and self-avoiding polygons

We give an algorithm for counting self-avoiding walks or self-avoiding p...

0 Samuel Zbarsky, et al. ∙

∙ 07/01/2019

Strong equivalences of approximation numbers and tractability of weighted anisotropic Sobolev embeddings

In this paper, we study multivariate approximation defined over weighted...

0 JiDong Hao, et al. ∙

∙ 08/13/2018

Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers

The first problem addressed by this article is the enumeration of some f...

0 Nicholas R. Beaton, et al. ∙

∙ 02/11/2022

Product-Coproduct Prographs and Triangulations of the Sphere

In this paper, we explain how the classical Catalan families of objects ...

0 Nicolas Borie, et al. ∙

∙ 08/11/2019

Bijective recurrences concerning two Schröder triangles

Let r(n,k) (resp. s(n,k)) be the number of Schröder paths (resp. little ...

0 Shishuo Fu, et al. ∙