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arXiv · 1905.10875

Permutations of type $B$ with fixed number of descents and minus signs

Katarzyna Kril·Wojciech Młotkowski
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Abstract

We study three dimensional array of numbers $B(n,k,j)$, $0\le j,k\le n$, where $B(n,k,j)$ is the number of type $B$ permutations of order $n$ with $k$ descents and $j$ minus signs. We prove in particular, that $b(n,k,j):=B(n,k,j)/\binom{n}{j}$ is an integer and provide two combinatorial interpretations for these numbers.

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Katarzyna Kril, Wojciech Młotkowski. 2019-05-26. Permutations of type $B$ with fixed number of descents and minus signs. https://arxiv.org/abs/1905.10875

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