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Chinese syzygies by insertions

Nohra Hage 1 Philippe Malbos 1 
1 AGL - Algèbre, géométrie, logique
ICJ - Institut Camille Jordan [Villeurbanne]
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.
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Submitted on : Sunday, November 21, 2021 - 1:04:43 AM
Last modification on : Tuesday, April 26, 2022 - 4:12:20 PM


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Nohra Hage, Philippe Malbos. Chinese syzygies by insertions. Semigroup Forum, Springer Verlag, In press, ⟨10.1007/s00233-021-10244-4⟩. ⟨hal-02015084v2⟩



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