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- W2962993088 abstract "For every finite Coxeter group Γ, each positive braid in the corresponding braid group admits a unique decomposition as a finite sequence of elements of Γ, the so-called Garside-normal form. The study of the associated adjacency matrix Adj(Γ) allows to count the number of Garside-normal form of a given length. In this paper we prove that the characteristic polynomial of Adj(Bn) divides the one of Adj(Bn+1). The key point is the use of a Hopf algebra based on signed permutations. A similar result was already known for the type A. We observe that this does not hold for type D. The other Coxeter types (I, E, F and H) are also studied." @default.
- W2962993088 created "2019-07-30" @default.
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- W2962993088 date "2017-11-01" @default.
- W2962993088 modified "2023-09-25" @default.
- W2962993088 title "A divisibility result in combinatorics of generalized braids" @default.
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- W2962993088 doi "https://doi.org/10.1016/j.jcta.2017.06.010" @default.
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