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Journal Articles Semigroup Forum Year : 2021

Chinese syzygies by insertions

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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Dates and versions

hal-02015084 , version 1 (12-02-2019)
hal-02015084 , version 2 (21-11-2021)

Identifiers

Cite

Nohra Hage, Philippe Malbos. Chinese syzygies by insertions. Semigroup Forum, In press, 104 (1), pp.88-108. ⟨10.1007/s00233-021-10244-4⟩. ⟨hal-02015084v2⟩
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