English

A new Boolean matrix representation for Catalan semirings

Rings and Algebras 2026-01-14 v2 Combinatorics Group Theory

Abstract

We construct a faithful representation of the semiring of all order-preserving decreasing transformations of a chain with n+1n+1 elements by Boolean upper triangular n×nn\times n-matrices.

Keywords

Cite

@article{arxiv.2510.05045,
  title  = {A new Boolean matrix representation for Catalan semirings},
  author = {Mikhail Volkov},
  journal= {arXiv preprint arXiv:2510.05045},
  year   = {2026}
}

Comments

8 pages, 3 figures. In version 2, the bibliography has been updated

R2 v1 2026-07-01T06:19:35.439Z