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- W3189368434 abstract "For a finite subset $A$ of $mathbb{Z}_{>0}$, Lazar and Wachs (2019) conjectured that the number of cycles on $A$ with only even-odd drops is equal to the number of D-cycles on $A$. In this note, we introduce cycles on a multiset with only even-odd drops and prove bijectively a multiset version of their conjecture. As a consequence, the number of cycles on $[2n]$ with only even-odd drops equals the Genocchi number $g_n$. With Laguerre histories as an intermediate structure, we also construct a bijection between a class of permutations of length $2n-1$ known to be counted by $g_n$ invented by Dumont and the cycles on $[2n]$ with only even-odd drops." @default.
- W3189368434 created "2021-08-16" @default.
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- W3189368434 date "2021-08-08" @default.
- W3189368434 modified "2023-09-27" @default.
- W3189368434 title "Cycles on a multiset with only even-odd drops" @default.
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- W3189368434 doi "https://doi.org/10.48550/arxiv.2108.03790" @default.
- W3189368434 hasPublicationYear "2021" @default.
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