Chinese syzygies by insertions
Combinatorics
2022-02-01 v3
Abstract
We construct a finite convergent semi-quadratic presentation for the Chinese monoid by adding column generators and using combinatorial properties of insertion algorithms on Chinese staircases. We extend this presentation into a coherent one whose generators are columns, rewriting rules are defined by insertion algorithms, and whose syzygies are defined as relations among insertion algorithms. Such a coherent presentation is used for representations of Chinese monoids, in particular, it is a way to describe actions of Chinese monoids on categories.
Keywords
Cite
@article{arxiv.1901.09879,
title = {Chinese syzygies by insertions},
author = {Nohra Hage and Philippe Malbos},
journal= {arXiv preprint arXiv:1901.09879},
year = {2022}
}