PreprintCC BY-NC-SA 4.0arXiv
The tableaux monoid: a rewriting-theoretic approach
Abstract
We study the tableaux monoid from the perspective of rewriting theory. We first construct a finite quadratic convergent presentation based on column generators and prove that it yields a biautomatic structure. We then extend this presentation to a finite coherent presentation in the sense of polygraphic rewriting. These results provide canonical normal forms, yield homological and algorithmic consequences, and produce a higher-dimensional presentation that can be used to describe actions of the tableaux monoid on categories.
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BibTeX
@misc{hage2026tableaux,
title = {{The tableaux monoid: a rewriting-theoretic approach}},
author = {Nohra Hage},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10035},
eprint = {2610.10035},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10035},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - The tableaux monoid: a rewriting-theoretic approach
AU - Nohra Hage
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10035
UR - https://arxiv.org/abs/2610.10035
AB - We study the tableaux monoid from the perspective of rewriting theory. We first construct a finite quadratic convergent presentation based on column generators and prove that it yields a biautomatic structure. We then extend this presentation to a finite coherent presentation in the sense of polygraphic rewriting. These results provide canonical normal forms, yield homological and algorithmic consequences, and produce a higher-dimensional presentation that can be used to describe actions of the tableaux monoid on categories.
ER -