Related papers: Primely generated refinement monoids
We extend Mullin's prime-generating procedures to produce sequences of primes lying in given residue classes. In particular we study the sequences generated by cyclotomic polynomials $\Phi_m(cx)$ for suitable $c\in\mathbb{Z}$. Under the…
We calculate the cluster modular groups of affine and doubly extended typecluster algebras in a uniform way by introducing a new family of quivers. We use this uniformdescription to construct a natural finite quotient of the cluster complex…
The notion of $n$-normal residuated lattice, as a class of residuated lattices in which every prime filter contains at most $n$ minimal prime filters, is introduced and studied. Before that, the notion of $\omega$-filter is introduced and…
In this short note, we describe generating sets for the monoids of consisting of all $2 \times 2$ matrices over certain finite tropical semirings.
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is…
The aim of this work is the study of the class of periodic parallelogram polyominoes, and two of its variantes. These objets are related to 321-avoiding affine permutations. We first provide a bijection with the set of triangles under Dyck…
In this paper we detail a number of properties of the affine line of a derivator, including a number of morphisms between $\mathbb{D}$ and $\mathbb{A}^1_{\mathbb{D}}$, a monoidal structure on $\mathbb{A}^1_{\mathbb{D}}$ if $\mathbb{D}$ is…
This work focuses on the combinatorial properties of glued semigroups and provides its combinatorial characterization. Some classical results for affine glued semigroups are generalized and some methods to obtain glued semigroups are…
We develop Morita theory of monoids in a closed symmetric monoidal category, in the context of enriched category theory.
We provide every Renner monoids with a monoid presentation, and we introduce a length function which extends the Coxeter length function.
We propose new conjectures about the relationship between the principal blocks of finite groups for different primes and establish evidence for these conjectures.
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…
Let $R$ be a Noetherian ring and $x_1,\ldots,x_t$ a permutable regular sequence of elements in $R$. Then there exists a finite set of primes $\Lambda$ and natural number $C$ so that for all $n_1,\ldots,n_t$ there exists a primary…
New nilpotent series are produced that refine the usual nilpotent series of a group. These refinements can be arbitrarily longer than the series they refine and therefore clarify in greater detail the structure of automorphisms of nilpotent…
This paper investigates the class of finitely presented monoids defined by homogeneous (length-preserving) relations from a computational perspective. The properties of admitting a finite complete rewriting system, having finite derivation…
Using notions of composita and composition of generating functions we obtain explicit formulas for Chebyshev polynomials, Legendre polynomials, Gegenbauer polynomials, Associated Laguerre polynomials, Stirling polynomials, Abel polynomials,…
In this paper, we study several topics on additive decompositions of primitive elemements in finite fields. Also we refine some bounds obtained by Dartyge and S\'{a}rk\"{o}zy and Shparlinski.
Prime number multiplet classifications and patterns are extended to negative integers. The extension from prime numbers to single prime powers is also studied. Prime number septets at equal distance are given. It is also shown that each…
We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.
Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic…