Garside combinatorics for Thompson’s monoid F + and a hybrid with the braid monoid B +
Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 683-709.

On the model of simple braids, defined to be the left divisors of Garside’s elements Δ n in the monoid B + , we investigate simple elements in Thompson’s monoid F + and in a larger monoid H + that is a hybrid of B + and F + : in both cases, we count how many simple elements left divide the right lcm of the first n-1 atoms, and characterize their normal forms in terms of forbidden factors. In the case of H + , a generalized Pascal triangle appears.

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DOI: 10.5802/alco.52
Classification: 05E15, 20M05, 20E22, 68Q42
Keywords: presented monoid, divisibility relation, simple elements, Thompson’s group, braid group, normal form, Garside element, directed animal
Dehornoy, Patrick 1; Tesson, Emilie 1

1 Université de Caen Laboratoire de Mathématiques Nicolas Oresme UMR 6139 14032 Caen, France
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Dehornoy, Patrick; Tesson, Emilie. Garside combinatorics for Thompson’s monoid $F^+$ and a hybrid with the braid monoid $B_{\infty }^{+}$. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 683-709. doi : 10.5802/alco.52. http://www.numdam.org/articles/10.5802/alco.52/

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