Plactic-like monoids arising from meets and joins of stalactic and taiga congruences

2023/09/18 by Thomas Aird, Aird, Thomas, Duarte Ribeiro +1 · 1 citation
Computer Science · Mathematics · #16T30 #20M05 (Primary) 05E16 #20M07 (Secondary) #20M35 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2309.10184

openalex publication_date 2023/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the four plactic-like monoids that arise by taking the meets and joins of stalactic and taiga congruences. We obtain the combinatorial objects associated with the meet monoids, establishing Robinson-Schensted-like correspondences and giving extraction and iterative insertion algorithms for these objects. We then obtain results on the sizes of classes of words equal in plactic-like monoids, show that some of these monoids are syntactic, and characterise their equational theories.

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