Related papers: The Stylic Monoid

This paper makes a combinatorial study of the two monoids and the two types of tableaux that arise from the two possible generalizations of the Patience Sorting algorithm from permutations (or standard words) to words. For both types of…

Let $A$ be the $n$-th Weyl algebra over a field of characteristic zero, and $\varphi:A\rightarrow A$ an endomorphism with $S = \varphi(A)$. We prove that if $A$ is finitely generated as a left or right $S$-module, then $S = A$. The proof…

There are left and right actions of the 0-Hecke monoid of the affine symmetric group $\tilde{S}_n$ on involutions whose cycles are labeled periodically by nonnegative integers. Using these actions we construct two bijections, which are…

We estimate the number $|\mathcal{A}_{\boldsymbol\lambda}|$ of elements on a nonlinear family $\mathcal{A}$ of monic polynomials of $\mathbb{F}_q[T]$ of degree $r$ having factorization pattern…

If a finitely generated monoid M is defined by a finite number of degree-preserving relations, then it has linear growth if and only if it can be decomposed into a finite disjoint union of subsets (which we call "sandwiches") of the form…

Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…

Clones are specializations of operads forming powerful instruments to describe varieties of algebras wherein repeating variables are allowed in their equations. They allow us in this way to realize and study a large range of algebraic…

This paper deals with the algebraic structure of the sequence of harmonics when combined with equal temperaments. Fractals and the golden ratio appear surprisingly on the way. The sequence of physical harmonics is an increasingly enumerable…

We consider an involution on the affine Weyl group of type $A$ induced from the nontrivial automorphism on the (finite) Dynkin diagram. We prove that the number of left cells fixed by this involution in each two-sided cell is given by a…

Let $X$ be a monoid scheme. We will show that the stalk at any point of $X$ defines a point of the topos $\Qc(X)$ of quasi-coherent sheaves over $X$. As it turns out, every topos point of $\Qc(X)$ is of this form if $X$ satisfies some…

We explain two related constructions on the data of two monoidal symmetric closed categories $\mathscr{A}$ and $\mathscr{E}$ and monoidal functors $F: \mathscr{E}\to \mathscr{A}$ and $G: \mathscr{A}\to \mathscr{E}$. In a first part, we…

We show how the categorial approach to inverse monoids can be described as a certain endofunctor (which we call the partialization functor) of some category. In this paper we show that this functor can be used to obtain several recently…

In any symmetric monoidal category, the $n$-th (co)equalizer symmetric power of an object $A$ is the (co)equalizer of all the permutations from $A^{\otimes n}$ to itself. If the symmetric monoidal category is $\mathbb{Q}_{\ge 0}$-linear,…

We show that the image of a subshift $X$ under various injective morphisms of symbolic algebraic varieties over monoid universes with algebraic variety alphabets is a subshift of finite type, resp. a sofic subshift, if and only if so is…

A numerical monoid is a cofinite additive submonoid of the nonnegative integers, while a Puiseux monoid is an additive submonoid of the nonnegative cone of the rational numbers. Using that a Puiseux monoid is an increasing union of copies…

Given a (finite or infinite) subset $X$ of the free monoid $A^*$ over a finite alphabet $A$, the rank of $X$ is the minimal cardinality of a set $F$ such that $X \subseteq F^*$. A submonoid $M$ generated by $k$ elements of $A^*$ is…

In this note, we give a characterisation in terms of identities of the join of $\mathbf{V}$ with the variety of finite locally trivial semigroups $\mathbf{LI}$ for several well-known varieties of finite monoids $\mathbf{V}$ by using…

In an atomic, cancellative, commutative monoid, the \omega-value measures how far an element is from being prime. In numerical monoids, we show that this invariant exhibits eventual quasilinearity (i.e., periodic linearity). We apply this…

Let u be a word over the positive integers. Motivated in part by a question from representation theory, we study the centralizer set of u which is C(u) = {w | uw is Knuth-equivalent to wu}. In particular, we give various necessary…

We say that a topological monoid $S$ is left non-archimedean (in short: l-NA) if the left action of $S$ on itself admits a proper $S$-compactification $\nu \colon S \hookrightarrow Y$ such that $Y$ is a Stone space. This provides a natural…