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- W3093167322 abstract "The alternating-runs polynomial enumerates alternating runs in the symmetric group. There are three formulae for the number of permutations, $R_{n,k}$ in $mathfrak{S}_n$ with $k$ alternating runs, but all of them are complicated. We show that when enumerated with sign taken into account, one gets a {it neat formula}. As a consequence, we get a near refinement of a result of Wilf on the exponent of $(1+t)$ when it divides the alternating-runs polynomial in the alternating group $mathcal{A}_n$. Other applications include a moment-type identity and enumeration of alternating permutations in $mathcal{A}_n$. Similar results are obtained for the type B and type D Coxeter groups." @default.
- W3093167322 created "2020-10-22" @default.
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- W3093167322 date "2020-10-19" @default.
- W3093167322 modified "2023-09-27" @default.
- W3093167322 title "Signed Alternating-runs enumeration in Classical Weyl Groups." @default.
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