C-trees and a coherent presentation for the plactic monoid of type C
Uran Meha

TL;DR
This paper introduces a new combinatorial and algebraic framework for the plactic monoid of type C, using decorated columns, coherent presentations, and C-trees to simplify calculations and analyze the structure of relations.
Contribution
It develops a finite convergent presentation for the type C plactic monoid, extends it to a coherent presentation, and introduces C-trees to parameterize highest weight words, simplifying the insertion algorithm.
Findings
Generated 3-cells have shape at most (4,3)
Column presentation of Pl(Cn) has 3-cells of shape at most (4,3)
Contrasts with type A where 3-cells are at most (3,3)
Abstract
In this article we introduce the decorated plactic monoid of type , denoted , via a finite convergent presentation , with generating set consisting of admissible columns, and an element . By Squier's coherent completion theorem, this presentation is extended into a coherent presentation by identifying a family of generating confluences, i.e. generating cells. Here the generating cells are critical branchings on words of length . We adapt the notions of crystal structure to , and show that the shape of cells is preserved by the action of Kashiwara operators. Thus we reduce the study of the coherent presentation to only describing the generating cells whose source is a word of highest weight. We then introduce combinatorial objects called trees which parameterize the words of highest…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Advanced Topics in Algebra
