Moscow Mathematical Journal

Volume 24, Issue 3, July–September 2024 pp. 321–355.

Ramified Inverse and Planar Monoids

Authors: Francesca Aicardi (1), Diego Arcis (2), and Jesús Juyumaya (3)
Author institution:(1) Sistiana Mare 56, 34011 Trieste, Italy
(2) Departamento de Matemáticas, Universidad de La Serena, Cisternas 1200, 1700000 La Serena, Chile
(3) Instituto de Matemáticas, Universidad de Valparaíso, Gran Bretaña 1111, 2340000 Valparaíso, Chile

Summary:

Ramified monoids are a class of monoids introduced by the authors. The main motivation for considering these monoids comes from knot theory. Earlier we have studied the ramified monoids of the symmetric group and of the Brauer monoid, among others. This paper studies the ramified monoid of the inverse symmetric monoid, which plays a notable role in knot theory as well. Here is also introduced the notion of planar ramified monoid. In particular, we give presentations for some planar ramified monoids arising from noncrossing set partitions.

2020 Math. Subj. Class. 20F05, 20M18, 20M20, 05A18, 20F36, 57K99, 20C08.

Keywords: Ramified monoids, ramified partitions, algebra of braids and ties.

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