Chinese syzygies by insertions

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...

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Bibliographic Details
Published in:Semigroup forum 2022-02, Vol.104 (1), p.88-108
Main Authors: Hage, Nohra, Malbos, Philippe
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Combinatorial analysis
Combinatorics
Generators
Insertion
Mathematics
Mathematics and Statistics
Monoids
Research Article
Staircases
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-021-10244-4