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- W3199430734 abstract "In this paper, we prove six conjectures on the evaluations of permanents, relating them to Genocchi numbers of the first and second kinds as well as (binomial) Euler numbers. For example, we prove that $$mathrm{per}left[leftlfloorfrac{2j-k}{n}rightrfloorright]_{1le j,kle n}=2(2^{n+1}-1)B_{n+1},$$ where $lfloorcdotrfloor$ is the floor function and $B_0,B_1,ldots$ are the Bernoulli numbers. This was previously conjectured by the third author. Various permutation statistics are at the heart of our approaches." @default.
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- W3199430734 date "2021-09-23" @default.
- W3199430734 modified "2023-10-12" @default.
- W3199430734 title "Proof of several conjectures relating permanents to combinatorial sequences" @default.
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- W3199430734 doi "https://doi.org/10.48550/arxiv.2109.11506" @default.
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