A bijective proof of a generalization of the non-negative crank--odd mex identity - Archive ouverte HAL
Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2023

A bijective proof of a generalization of the non-negative crank--odd mex identity

Résumé

Recent works of Andrews--Newman and Hopkins--Sellers unveil an interesting relation between two partition statistics, the crank and the mex. They state that, for a positive integer $n$, there are as many partitions of $n$ with non-negative crank as partitions of $n$ with odd mex. In this paper, we give a bijective proof of a generalization of this identity provided by Hopkins, Sellers, and Stanton. Our method uses an alternative definition of the Durfee decomposition, whose combinatorial link to the crank was recently studied by Hopkins, Sellers, and Yee.

Dates et versions

hal-03916647 , version 1 (30-12-2022)

Identifiants

Citer

Isaac Konan. A bijective proof of a generalization of the non-negative crank--odd mex identity. The Electronic Journal of Combinatorics, 2023, 30 (1), ⟨10.37236/11472⟩. ⟨hal-03916647⟩
26 Consultations
0 Téléchargements

Altmetric

Partager

More