On Kiselman quotients of 0-Hecke monoids

By Olexandr Ganyushkin, Volodymyr Mazorchuk. 2010

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Combining the definition of 0-Hecke monoids with that of Kiselman semigroups, we define what we call Kiselman quotients of 0-Hecke monoids associated with simply laced Dynkin diagrams. We classify these monoids up to isomorphism, determine their idempotents and show that they are $\mathcal{J}$-trivial. For type $A$ we show that Catalan numbers appear as the maximal cardinality of our monoids, in which case the corresponding monoid is isomorphic to the monoid of all order-preserving and order-decreasing total transformations on a finite chain. We construct various representations of these monoids by matrices, total transformations and binary relations. Motivated by these results, with a mixed graph we associate a monoid, which we call a Hecke-Kiselman monoid, and classify such monoids up to isomorphism. Both Kiselman semigroups and Kiselman quotients of 0-Hecke monoids are natural examples of Hecke-Kiselman monoids.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bd17b13d688b266421c88997757215f9b48915aa

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In Computational Theory and Mathematics

  1. Ben Steinberg
  2. Stuart W. Margolis
  3. Mark V. Lawson
  4. L. O. Clark
  5. Aidan Sims
  6. Enrique Pardo
  7. R. Exel
  8. John L. Rhodes

In Discrete Mathematics and Combinatorics

  1. Stuart W. Margolis
  2. Ben Steinberg

In Geometry and Topology

  1. Stuart W. Margolis
  2. Ben Steinberg
  3. Mark V. Lawson
  4. L. O. Clark
  5. Aidan Sims
  6. R. Exel
  7. Enrique Pardo
  8. Daniel Lenz

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