8 citations · 11 across the 5 of their papers we have counts for
5 papers
Simple solutions of the Yang-Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +1
We study simple set-theoretic solutions of the Yang-Baxter equation that are finite and non-degenerate. Such retractable solutions are fully described and to investigate the irretr…
Finite idempotent set-theoretic solutions of the Yang--Baxter equation
Ilaria Colazzo, Eric Jespers, Łukasz Kubat +2
It is proven that finite idempotent left non-degenerate set-theoretic solutions of the Yang-Baxter equation on a set are determined by a left simple semigroup structure…
The structure monoid and algebra of a non-degenerate set-theoretic solution of the Yang-Baxter equation
Eric Jespers, Łukasz Kubat, Arne Van Antwerpen
For a finite involutive non-degenerate solution of the Yang--Baxter equation it is known that the structure monoid is a monoid of I-type, and the structure algebra…
A note on identities in plactic monoids and monoids of upper-triangular tropical matrices
Alan J. Cain, Georg Klein, Łukasz Kubat +2
This paper uses the combinatorics of Young tableaux to prove the plactic monoid of infinite rank does not satisfy a non-trivial identity, by showing that the plactic monoid of rank…
Grobner-Shirshov bases for plactic algebras
Lukasz Kubat, Jan Okninski
A finite Grobner-Shirshov basis is constructed for the plactic algebra of rank 3 over a field K. It is also shown that plactic algebras of rank exceeding 3 do not have finite Grobn…