A new Boolean matrix representation for Catalan semirings

2025/10/06 by Mikhail V. Volkov, Volkov, Mikhail
Computer Science · Engineering · #06F05 #15B34 #16Y60 #20M20 #Advanced Control Systems Optimization #Combinatorics (math.CO) #FOS: Mathematics #Formal Methods in Verification #Fuzzy Logic and Control Systems #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2510.05045

openalex publication_date 2025/10/06 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Identities of triangular Boolean matrices
• Catalan monoids inherently nonfinitely based relative to finite R-trivial semigroups
• Catalan monoids inherently nonfinitely based relative to finite R -trivial semigroups
• Identities in unitriangular and gossip monoids
• The Hecke group algebra of a Coxeter group and its representation theory

Related

• Semiring identities of semigroups of reflexive relations and upper triangular boolean matrices
• Identities of triangular Boolean matrices
• Four transformations on the Catalan triangle
• Linear isomorphisms preserving Green's relations for matrices over\n semirings
• Associative, idempotent, symmetric, and order-preserving operations on\n chains