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arxiv: 1905.10875 · v1 · pith:WH5WLOAOnew · submitted 2019-05-26 · 🧮 math.CO

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

classification 🧮 math.CO
keywords descentsminusnumbernumberspermutationssignstypearray
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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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