On the model of simple braids, defined to be the left divisors of Garside’s elements in the monoid , we investigate simple elements in Thompson’s monoid and in a larger monoid that is a hybrid of and : in both cases, we count how many simple elements left divide the right lcm of the first atoms, and characterize their normal forms in terms of forbidden factors. In the case of , a generalized Pascal triangle appears.
Accepted:
Published online:
DOI: https://doi.org/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
@article{ALCO_2019__2_4_683_0,
author = {Dehornoy, Patrick and Tesson, Emilie},
title = {Garside combinatorics for Thompson{\textquoteright}s monoid $F^+$ and a hybrid with the braid monoid $B_{\infty }^{+}$},
journal = {Algebraic Combinatorics},
pages = {683--709},
publisher = {MathOA foundation},
volume = {2},
number = {4},
year = {2019},
doi = {10.5802/alco.52},
zbl = {1422.05106},
language = {en},
url = {https://alco.centre-mersenne.org/articles/10.5802/alco.52/}
}
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. https://alco.centre-mersenne.org/articles/10.5802/alco.52/
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