Deciding conjugacy in sylvester monoids and other homogeneous monoids
TLDR
It is proved that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoid.Abstract:
We give a combinatorial characterization of conjugacy in the sylvester monoid, showing that conjugacy is decidable for this monoid. We then prove that conjugacy is undecidable in general for homogeneous monoids and even for multihomogeneous monoids.read more
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Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
TL;DR: This paper studies complete rewriting systems and biautomaticity for three interesting classes of finite-rank homogeneous monoids: Chinese monoid, hypoplactic monoids, and sylvester monoids; the monoid algebras corresponding to monoids of these classes are automaton algeBRas in the sense of Ufnarovskij.
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Crystal monoids & crystal bases: rewriting systems and biautomatic structures for plactic monoids of types An, Bn, Cn, Dn, and G2
TL;DR: This paper constructs presentations via finite complete rewriting systems for Plactic monoids of types A, B, C, and D using a unified proof strategy that depends on Kashiwara's crystal bases and analogies of Young tableaux, and on Lecouvey's presentations for these monoids.
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Equations and first-order theory of one-relator and word-hyperbolic monoids
Albert Garreta,Rob Gray +1 more
TL;DR: In this paper, the first-order theory of one-relator monoids and word-hyperbolic monoids with length constraints has been investigated, and it has been shown that the decidability problem of word equations with length constraint is reducible to the Diophantine problem in any of these monoids.
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Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, Baxter, and related monoids
Alan J. Cain,António Malheiro +1 more
TL;DR: In this article, the maximum diameter of a connected component of the cyclic shift graph of these monoids in the rank-n case was studied, and the current state-of-the-art results are summarized in a table.
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Combinatorics of cyclic shifts in plactic, hypoplactic, sylvester, and related monoids
Alan J. Cain,António Malheiro +1 more
TL;DR: New results on the diameters of connected components of the cyclic shift graphs of the finite-rank analogues of these monoids are discussed, showing that the maximum diameter of a connected component is dependent only on the rank.
References
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Book
Introduction to Automata Theory, Languages, and Computation
TL;DR: This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Book
Algebraic Combinatorics on Words
TL;DR: In this article, Berstel and Perrin proposed the concept of Sturmian words and the plactic monoid, which is a set of permutations and infinite words.
Book
String-rewriting systems
Ronald V. Book,Friedrich Otto +1 more
TL;DR: This chapter provides formal definitions of string-rewriting systems and their induced reduction relations and Thue congruences and relies on Section 1.4 for basic definitions and notation for strings.
Journal ArticleDOI
Hopf Algebra of the Planar Binary Trees
Jean-Louis Loday,Maria O. Ronco +1 more
TL;DR: In this article, a basis Qn of Soln is defined such that the composite map k[Qn]&Soln k[Sn] has the following property: its linear dual k[ Sn] k[SN] is induced by a set-theoretic map Sn Qn in between Sn and Qn there is an intermediate set Yn, which is made of planar binary trees with n vertices.