Matchings avoiding partial patterns and lattice paths

Vít Jelínek; Nelson Y. Li; Toufik Mansour; Sherry H.F. Yan

doi:10.37236/1115

Matchings avoiding partial patterns and lattice paths

Vít Jelínek
, Nelson Y. Li
, Toufik Mansour
, Sherry H.F. Yan

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123-avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). As a consequence, the refined enumeration of 1123-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between 1132-avoiding matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step, which may go under the x-axis.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Electronic Journal of Combinatorics
Volume	13
Issue number	1 R
DOIs	https://doi.org/10.37236/1115
State	Published - 19 Oct 2006

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics
Applied Mathematics

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10.37236/1115

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AU - Mansour, Toufik

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N2 - In this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123-avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). As a consequence, the refined enumeration of 1123-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between 1132-avoiding matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step, which may go under the x-axis.

AB - In this paper, we consider matchings avoiding partial patterns 1123 and 1132. We give a bijection between 1123-avoiding matchings with n edges and nonnegative lattice paths from (0, 2) to (2n, 0). As a consequence, the refined enumeration of 1123-avoiding matchings can be reduced to the enumeration of certain lattice paths. Another result of this paper is a bijection between 1132-avoiding matchings with n edges and lattice paths from (0, 0) to (2n, 0) starting with an up step, which may go under the x-axis.

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Matchings avoiding partial patterns and lattice paths

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