Related papers: On finite generating sets of infinitely generated …

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…

In this short note, we are interested in discussing characteristics of finite generating sets for $\mathcal{F}$, the set of all semiflows with non negative coefficients of a Petri Net. By systematically positioning these results over semi…

We review some recent results related to the self-assembly of infinite structures in the Tile Assembly Model. These results include impossibility results, as well as novel tile assembly systems in which shapes and patterns that represent…

In this article we fully describe the domain of the infinitesimal generator of the optimal state semigroup which arises in the theory of the linear-quadratic problem for a specific class of boundary control systems. This represents an…

It is well-known that characters classify linear representations of finite groups, that is if characters of two representations of a finite group are the same, these representations are equivalent. It is also well-known that, in general,…

The recent surge in interest in city layout generation underscores its significance in urban planning and smart city development. The task involves procedurally or automatically generating spatial arrangements for urban elements such as…

We present a construction that gives an infinite series of divisible design graphs which are Cayley graphs.

In commutative ring theory, there is a theorem of Cohen which states that if in a commutative ring all prime ideals are finitely generated then every ideal is finitely generated. However, it is known that having only maximal ideals finitely…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

Text-to-image generative models have enabled high-resolution image synthesis across different domains, but require users to specify the content they wish to generate. In this paper, we consider the inverse problem -- given a collection of…

We study a family of finitely generated residually finite groups. These groups are doubles $F_2*_H F_2$ of a rank-$2$ free group $F_2$ along an infinitely generated subgroup $H$. Varying $H$ yields uncountably many groups up to isomorphism.

Continuing earlier work, we show how to realize irreducible finite-dimensional representations of the complex group of type $G_2$ via tableaux, along the way exhibiting explicit generators of the defining ideal of the flag variety

Let $U/L$ be a finite abelian extension of number fields. We first construct a universal primitive generator of $U$ over $L$ whose relative trace to any intermediate field $F$ becomes a generator of $F$ over $L$, too. We also develop a…

Quadratic harnesses are time-inhomogeneous Markov polynomial processes with linear conditional expectations and quadratic conditional variances with respect to the past-future filtrations. Typically they are determined by five numerical…

We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

A generating set $S$ for a group $G$ is independent if the subgroup generated by $S\setminus \{s\}$ is properly contained in $G$, for all $s \in S.$ In this paper, we study a problem proposed by Peter Glasby: we investigate finite groups,…

We present in this paper a routine which construct the ideal generated by a list of elements in a matrix Lie algebra at any particular characteristic. We have used this algorithm to analyze the problem of the simplicity of some Lie…

Two minimal generating sets of the first syzygies of a monomial ideal are produced, given the minimal generating set of the ideal.

We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these…