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- W2300425115 abstract "Let $G_{M}^{+}$ be the Artin monoid of finite type generated by the letters $a_i, iin I$ with respect to a Coxeter matrix $M$ that is equipped with the degree map $°!:!G_{M}^{+} to!Z_{ge0}$ defined by assigning to each equivalence class of words the length of the words, and let $N_{M, °}(t)!:=!!sum_{J subset I}(-1)^{#J} t^{°(Delta_{J})}$ be the skew-growth function, where the summation index $J$ runs over all subsets of $I$ and $Delta_{J}$ is the fundamental element in $G_{M}^{+}$ associated to the set $J$. In this article, we will calculate the derivative at $t = 1$ of the polynomial $N_{M, °}(t)$. As a result, we show that the polynomial $N_{M, °}(t)$ has a simple root at $t = 1$." @default.
- W2300425115 created "2016-06-24" @default.
- W2300425115 creator A5070375397 @default.
- W2300425115 date "2016-03-15" @default.
- W2300425115 modified "2023-09-27" @default.
- W2300425115 title "On the derivative at $t = 1$ of the skew-growth functions for Artin monoids" @default.
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