Related papers: Bases for counting functions on free monoids and g…
Measure free factors are a generalization of the notion of free factors of a group, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by…
The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…
In the paper "Triangulations, orientals, and skew monoidal categories", the free monoidal category Fsk on a single generating object was described. We sharpen this by giving a completely explicit description of Fsk, and so of the free skew…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
Gr\"obner bases can be used for computing the Hilbert basis of a numerical submonoid. By using these techniques, we provide an algorithm that calculates a basis of a subspace of a finite-dimensional vector space over a finite prime field…
Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside's approach to Artin's braid groups, it has been extended to more and more…
Classically, Groebner bases are computed by first prescribing a set monomial order. Moss Sweedler suggested an alternative and developed a framework to perform such computations by using valuation rings in place of monomial orders. We build…
It is well known that in q-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward q-analogue of the classical axioms does not give a q-matroid. For this…
We construct a free group of continuum many generators among those autobijections of $\mathbb{R}$ which are also Hamel bases of $\mathbb{R}^2$, with identity function included. We also observe two new cases when a real function is a…
The first aim of this study is to define soft sequential compact metric spaces and to investigate some important theorems on soft sequential compact metric space. Second is to introduce net and totally bounded soft metric space and study…
The aim of this note is to introduce a compound basis for the space of symmetric functions. Our basis consists of products of Schur functions and $Q$-functions. The basis elements are indexed by the partitions. It is well known that the…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Electronic structure codes usually allow to calculate the work function as a part of the theoretical description of surfaces and processes such as adsorption thereon. This requires a proper calculation of the electrostatic potential in all…
We present the foundations of the theory of functions of bounded variation and sets of finite perimeter in abstract Wiener spaces.
This paper provides a preparatory introduction to torsors, written with a view toward later applications in the author's work. Rather than aiming at a comprehensive survey, the exposition focuses on those aspects of torsors that are most…
A wide variety of problems in combinatorics and discrete optimization depend on counting the set $S$ of integer points in a polytope, or in some more general object constructed via discrete geometry and first-order logic. We take a tour…
Developed by Buchberger for commutative polynomial rings, Groebner Bases are frequently applied to solve algorithmic problems, such as the congruence problem for ideals. Until now, these ideas have been transmitted to different in part…
We generalize presentations of the fundamental group of discriminant complements and arrive at a class of presentations associated naturally with words in the free monoid of the alphabet $\sigma_1,\dots,\sigma_{n-1}$. Our study addresses…