Related papers: Character theoretic techniques for nonabelian part…

The Gruenberg-Kegel graph ${\rm GK}(G)=(V_G, E_G)$ of a finite group $G$ is a simple graph with vertex set $V_G=\pi(G)$, the set of all primes dividing the order of $G$, and such that two distinct vertices $p$ and $q$ are joined by an edge,…

Finding upper bounds for character ratios is a fundamental problem in asymptotic group theory. Previous bounds in the symmetric group have led to remarkable applications in unexpected domains. The existing approaches predominantly relied on…

We study totally disconnected, locally compact (t.d.l.c.) groups from an algorithmic perspective. We give various approaches to defining computable presentations of t.d.l.c.\ groups, and show their equivalence. In the process, we obtain an…

We consider the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…

We analyze generalized progressions in some nonabelian groups using a measure of complexity called VC-dimension, which was originally introduced in statistical learning theory by Vapnik and Chervonenkis. Here by a "generalized progression"…

We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations…

We extend the Howlett-Isaacs theorem on the solvability of groups of central type taking into account actions by automorphisms. Then we study certain induced characters whose constituents have all the same degree.

Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new family of GDDs, which is also involved with a well-known…

Olmez, in "Symmetric $1\frac{1}{2}$-Designs and $1\frac{1}{2}$-Difference Sets" (2014), introduced the concept of a partial geometric difference set (also referred to as a $1\frac{1}{2}$-design), and showed that partial geometric difference…

We derive the asymptotic distribution of the domination number of a new family of random digraph called proximity catch digraph (PCD), which has application to statistical testing of spatial point patterns and to pattern recognition. The…

Let $G$ be a finite group. The bipartite divisor graph for the set of irreducible complex character degrees is the undirected graph with vertex set consisting of the prime numbers dividing some character degree and of the non-identity…

Let $k$ be a field of characteristic $p$, let $P$ be a finite $p$- group, where $p$ is an odd prime, and let $D(P)$ be the Dade group of endo-permutation $kP$-modules. It is known that $D(P)$ is detected via deflation--restriction by the…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…

Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…

Let $G$ be a finite group and $m$ be an integer. We employ the notation $g_i$ to represent elements $(g,i)$ in the Cartesian product $G \times \mathbb{Z}_m$, where $\mathbb{Z}_m$ denotes integers modulo $m$. For given sets $T_{i,j}…

Consider the algebraic dynamics on a torus T=G_m^n given by a matrix M in GL_n(Z). Assume that the characteristic polynomial of M is prime to all polynomials X^m-1. We show that any finite equivariant map from another algebraic dynamics…

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities…

This paper investigates the enumeration of Cayley digraphs, focusing on counting Cayley digraphs on dihedral groups up to CI-isomorphism. By leveraging the Cauchy-Frobenius Lemma and properties of automorphisms, we derive an explicit…