Related papers: A note on connecting multiplicative functions defi…
We give some connections between various functions defined on finitely presented groups (isoperimetric, isodiametric, Todd-Coxeter radius, filling length functions, etc.), and we study the relation between those functions and the…
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…
In this paper, we study polynomials of the form $f(x)=(x^n+x^{n-1}+...+1)^l$ for $l=1,2,3,4$ to generate a pattern titled "unique coefficient pattern". Namely, we analyze each unique coefficient patterns of $f(x)$ and generate functions…
This paper provides a realization of all classical and most exceptional finite groups of Lie type as Galois groups over function fields over F_q and derives explicit additive polynomials for the extensions. Our unified approach is based on…
It is observed that the conjugacy growth series of the infinite fini-tary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
The investigation and classification of non-unique factorization phenomena has attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P.A. Garc\'ia-S\'anchez, together with several co-authors, derived…
This paper surveys and develops links between polynomial invariants of finite groups, factorization theory of Krull domains, and product-one sequences over finite groups. The goal is to gain a better understanding of the multiplicative…
In this paper we investigate some properties of the Burnside ring of a profinite group as defined in \cite{ds}. We introduce the notion of the crossed Burnside ring of a profinite FC-group, and generalise some results from finite to…
We study selfadjoint functors acting on categories of finite dimensional modules over finite dimensional algebras with an emphasis on functors satisfying some polynomial relations. Selfadjoint functors satisfying several easy relations, in…
The multiplicative anomaly related to the functional regularized determinants involving products of elliptic operators is introduced and some of its properties discussed. Its relevance concerning the mathematical consistency is stressed.…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
In this note, presented as a ``community service", followed by the PhD research of the author, we draw the relation between Casselman's theorem regarding the asymptotic behavior of matrix coefficients of reductive algebraic groups over…
We compute the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the…
We describe the associative multilinear polynomial functions over commutative integral domains. This extends Marichal and Mathonet's result on infinite integral domains and provides a new proof of Andres's classification of two-element…
In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.
It is a well known result that the number of points over a finite field on the Legendre family of elliptic curves can be written in terms of a hypergeometric function modulo $p$. In this paper, we extend this result, due to Igusa, to a…
This paper introduces a set of finite summation formulas and utilize them to establish various functional relationships involving the multivariable Hurwitz-Lerch zeta function. Additionally, the paper examines several examples of these…
We derive a formula connecting the orders of the automorphism groups of a finite group and of its covering groups.
Sigmoid functions play an important role in many areas of applied mathematics, including machine learning, population dynamics and probability. We place the study of sigmoid functions in the context of the derivative sub-group of the group…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).