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

TL;DR

This paper explores four plactic-like monoids derived from stalactic and taiga congruences, establishing combinatorial correspondences, algorithms, and algebraic properties to understand their structure and classification.

Contribution

It introduces new plactic-like monoids from meets and joins of stalactic and taiga congruences, with combinatorial models and algebraic characterizations.

Findings

Established Robinson-Schensted-like correspondences for these monoids

Developed extraction and insertion algorithms for combinatorial objects

Characterized the sizes of equivalence classes and their algebraic properties

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.