ALGEBRAIC COMBINATORICS

no. 4

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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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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