19 citations · 143 across the 45 of their papers we have counts for
50 papers
Artin monoids, their homomorphisms and twins
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
Motivated by the twin homomorphism problem for Coxeter groups and the corresponding Hecke monoids, we find a large class of its solutions originating from standard homomorphisms of…
Hecke monoids, their homomorphisms and parabolicity
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
We study homomorphisms of Hecke monoids, notably parabolic homomorphisms, which map parabolic elements to parabolic elements, and injective ones. The importance of the first class…
Monomial bialgebras
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
Starting from a single solution of QYBE (or CYBE) we produce an infinite family of solutions of QYBE (or CYBE) parametrized by transitive arrays and, in particular, by signed permu…
Noncommutative marked surfaces II: tagged triangulations, clusters, and their symmetries
Arkady Berenstein, Min Huang, Vladimir Retakh
The aim of the paper is to define noncommutative cluster structure on several algebras related to marked surfaces possibly with orbifold points of various orders, wh…
Multiple Horn problems for planar networks and invertible matrices
Anton Alekseev, Arkady Berenstein, Anfisa Gurenkova +1
The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations and for a triple of invertible matrices with giv…
Hecke and Artin monoids and their homomorphisms
Arkady Berenstein, Jacob Greenstein, Jian-Rong Li
The aim of the present work is to systematically study homomorphisms of Hecke and Artin monoids and thus to develop their comprehensive theory. Our original motivation was the stri…