相关论文: Chinese syzygies by insertions

We construct finite coherent presentations of plactic monoids of type A. Such coherent presentations express a system of generators and relations for the monoid extended in a coherent way to give a family of generators of the relations…

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…

We introduce cyclic diagram monoids, a generalisation of classical diagram monoids that adds elements of arbitrary period by including internal components, with a view towards cryptography. We classify their simple representations and…

We study arithmetic properties of factorizations of elements into products of generators, in monoids given with explicit presentations. After relating and comparing this perspective to the more usual approach of factoring into products of…

This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoids, hypoplactic monoids, and sylvester monoids. For Chinese monoids, we first give new…

This paper explores the ability of the Chinese Remainder Theorem formalism to model Montgomery-type algorithms. A derivation of CRT based on Qin's Identity gives Montgomery reduction algorithm immediately. This establishes a unified…

In this paper, we describe an algorithm for computing the left, right, or 2-sided congruences of a finitely presented semigroup or monoid with finitely many classes, and an alternative algorithm when the finitely presented semigroup or…

Convergent rewriting systems are well-known tools in the study of the word-rewriting problem. In particular, a presentation of a monoid by a finite convergent rewriting system gives an algorithm to decide the word problem for this monoid.…

A finitely generated commutative monoid is uniquely presented if it has only a minimal presentation. We give necessary and sufficient conditions for finitely generated, combinatorially finite, cancellative, commutative monoids to be…

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

We propose a generic design for Chinese remainder algorithms. A Chinese remainder computation consists in reconstructing an integer value from its residues modulo non coprime integers. We also propose an efficient linear data structure, a…

All irreducible representations of the Chinese monoid $C_n$, of any rank $n$, over a nondenumerable algebraically closed field $K$, are constructed. It turns out that they have a remarkably simple form and they can be built inductively from…

We construct certain monoids, called tied monoids. These monoids result to be semidirect products finitely presented and commonly built from braid groups and their relatives acting on monoids of set partitions. The nature of our monoids…

In this article, how word embeddings can be used as features in Chinese sentiment classification is presented. Firstly, a Chinese opinion corpus is built with a million comments from hotel review websites. Then the word embeddings which…

We give a monoid presentation in terms of generators and defining relations for the partial analogue of the finite dual inverse symmetric monoid.

Rewriting methods have been developed for the study of coherence for algebraic objects. This consists in starting with a convergent presentation, and expliciting a family of generating confluences to obtain a coherent presentation -- one…

A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Confluent and terminating rewriting systems generate coherent presentations, whose relations among relations are defined by…

Distributed word representations are very useful for capturing semantic information and have been successfully applied in a variety of NLP tasks, especially on English. In this work, we innovatively develop two component-enhanced Chinese…

This paper introduces and studies a categorical analogue of the familiar monoid semiring construction. By introducing an axiomatisation of summation that unifies notions of summation from algebraic program semantics with various notions of…

It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…