Related papers: Identities of the stylic monoid
We will study the presentations of fundamental groups of the complement of complexified real affine line arrangements that do not contain two parallel lines. By Yoshinaga's minimal presentation, we can give positive homogeneous…
If $M$ is a submonoid of a finitely generated nilpotent group $G$, and $MG'$ is a finite index subgroup of $G$, then $M$ itself is a finite index subgroup of $G$. If $MG'=G$, then $M=G$. This generalizes a well-known theorem for subgroups…
Periodic solutions of the planar $N$-body problem determine braids through the trajectory of $N$ bodies. Braid types can be used to classify periodic solutions. According to the Nielsen-Thurston classification of surface automorphisms,…
We prove that the equality problem is decidable for rational subsets of the monogenic free inverse monoid $F$. It is also decidable whether or not a rational subset of $F$ is recognizable. We prove that a submonoid of $F$ is rational if and…
A finite semigroup is finitely related (has finite degree) if its term functions are determined by a finite set of finitary relations. For example, it is known that all nilpotent semigroups are finitely related. A nilpotent monoid is a…
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the…
By classical results of Malcev, cancellative monoids need not be group-embeddable. In this paper, we describe and give presentations for and study an infinite family $\mathcal{M}_n$ of cancellative monoids which are not group-embeddable,…
We provide a countable series of bisimple $\mathcal{H}$-trivial finitely presented congruence-free monoids.
We transform the method of Glasson into a sufficient condition under which a monoid is non-finitely related, add a new member to the collection of interlocking word-patterns, and use it to show that the monoid $M(ab^2a, a^2b^2)$ is…
We establish a new sufficient condition under which a monoid is non-finitely based and apply this condition to show that the 9-element monoid $L_4^1$ is non-finitely based. The monoid $L_4^1$ was the only unsolved case in the finite basis…
Building on the work of Gabriel Conant, we investigate the enumeration problems of finite distance monoids by applying the decomposition of Archimedean classes and studying their internal arithmetic progressions. Specifically, we first…
We prove that for every natural number n there exists a natural number N(n) such that every multilinear skew-symmetric polynomial on N(n) or more variables which vanishes in the free associative algebra vanishes as well in any n-generated…
Given an integer $M\geq 2$, we deploy the generating function techniques to compute the number of $M$-th roots of identity in some of the well-known finite groups of Lie type, more precisely for finite general linear groups, symplectic…
This paper considers whether non-trivial identities are satisfied by certain `plactic-like' monoids that, like the plactic monoid, are closely connected to combinatorics. New results show that the hypoplactic, sylvester, Baxter, stalactic,…
Let $H$ be a (multiplicatively written) monoid. The family $\mathcal{P}_{\text{fin},1}(H)$ of finite subsets of $H$ containing the identity element is itself a monoid when endowed with setwise multiplication induced by $H$. Tringali and Yan…
We study the four plactic-like monoids that arise by taking the meets and joins of stalactic and taiga congruences. We obtain the combinatorial objects associated with the meet monoids, establishing Robinson-Schensted-like correspondences…
Motivated by recent advances in inverse semigroup theory, we investigate the growth of and identities satisfied by free left and free two-sided adequate monoids. We explicitly compute the growth of the monogenic free left adequate monoid…
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
We construct a new monoid structure for Artin groups associated with finite Coxeter systems. This monoid shares with the classical positive braid monoid a crucial algebraic property: it is a Garside monoid. The analogy with the classical…
A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the…