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- W4299840431 abstract "We study the geodesic growth series of the braid group on three strands, B_3 := <a,b|aba = bab>. We show that the set of geodesics of B_3 with respect to the generating set S := {a,b,a^-1,b^-1} is a regular language, and we provide an explicit computation of the geodesic growth series with respect to this set of generators. In the process, we give a necessary and sufficient condition for a freely reduced word w in S^* to be geodesic in B_3 with respect to S. Also, we show that the translation length with respect to S of any element in B_3 is an integer." @default.
- W4299840431 created "2022-10-03" @default.
- W4299840431 creator A5091458368 @default.
- W4299840431 date "2003-11-10" @default.
- W4299840431 modified "2023-10-01" @default.
- W4299840431 title "Geodesics in the braid group on three strands" @default.
- W4299840431 doi "https://doi.org/10.48550/arxiv.math/0311153" @default.
- W4299840431 hasPublicationYear "2003" @default.
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