Geodesic
A bijective proof of a generalization of the non-negative crank-odd mex identity
Isaac Konan1
1University of Paris
The electronic journal of combinatorics, Tome 30 (2023) no. 1
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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.
DOI : 10.37236/11472
Classification : 11P84, 11P83, 05A17, 05A19
Mots-clés : integer partition, crank, mex

Isaac Konan  1

1 University of Paris 
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Isaac Konan. A bijective proof of a generalization of the non-negative crank-odd mex identity. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11472

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