Related papers: The Main Problem of Block Theory: Picky Elements a…

The paper develops a new technique to extract a characteristic subset from a random source that repeatedly samples from a set of elements. Here a characteristic subset is a set that when containing an element contains all elements that have…

We argue that fundamental objects in particle theory are not elementary particles and antiparticles but objects described by irreducible representations (IRs) of the de Sitter (dS) algebra. One might ask why, then, experimental data give…

The present paper describes some results on the Loewy series of the center of a modular group algebra in order to solve a problem on the number of irreducible ordinary characters. For instance, we prove that a $p$-block of a finite group…

The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…

In [1] it was shown that the Kochen Specker theorem can be written in terms of the non-existence of global elements of a certain varying set over the partially ordered set of boolean subalgebras of projection operators on some Hilbert…

Let $G$ be a finite group, $p$ a prime and $B$ a Brauer $p$-block of $G$ with defect group $D$. We prove that if the number of irreducible ordinary characters in $B$ is $5$ then $D\cong C_5, C_7, D_8$ or $Q_8$, assuming that the…

Extracting information from large graphs has become an important statistical problem since network data is now common in various fields. In this minicourse we will investigate the most natural statistical questions for three canonical…

In this article we overview those aspects of the theory of affine semigroups and their algebras that have been relevant for our own research, and pose several open problems. Answers to these problems would contribute substantially to the…

A new type of conjectures on characters of finite groups, related to the McKay conjecture, have recently been proposed. In this paper, we study these conjectures for symmetric groups.

A new conjecture on characters of finite groups, related to the McKay conjecture, was proposed recently by the first and third authors. In this paper, we prove it for $p$-solvable groups when $p$ is odd.

We study the problem of ranking with submodular valuations. An instance of this problem consists of a ground set $[m]$, and a collection of $n$ monotone submodular set functions $f^1, \ldots, f^n$, where each $f^i: 2^{[m]} \to R_+$. An…

K\"orner introduced the notion of graph entropy in 1973 as the minimal code rate of a natural coding problem where not all pairs of letters can be distinguished in the alphabet. Later it turned out that it can be expressed as the solution…

This paper will prove that: 1. $G$ has a block only having linear ordinary characters if and only if $G$ is a $p$-nilpotent group with an abelian Sylow $p$-subgroup; 2. $G$ has a block only having linear Brauer characters if and only if…

We show that the subgroup of the Picard group of a $p$-block of a finite group given by bimodules with endopermutation sources modulo the automorphism group of a source algebra is determined locally in terms of the fusion system on a defect…

The most developed aspect of the theory of finite semigroups is their classification in pseudovarieties. The main motivation for investigating such entities comes from their connection with the classification of regular languages via…

We study a new generalization of palindromes and gapped palindromes called block palindromes. A block palindrome is a string that becomes a palindrome when identical substrings are replaced with a distinct character. We investigate several…

Slattery has generalized Brauer's theory of p-blocks of finite groups to pi-blocks of pi-separable groups where pi is a set of primes. In this setting we show that the order of a defect group of a pi-block B is bounded in terms of the…

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we…

We prove the Alperin-McKay Conjecture for all $p$-blocks of finite groups with metacyclic, minimal non-abelian defect groups. These are precisely the metacyclic groups whose derived subgroup have order $p$. In the special case $p=3$, we…

Let p be a prime number, G a finite group, and A a finite group acting on G. The Brown poset of nonidentity p-subgroups of G is then an A-poset. We investigate the equivariant subposet and the equivariant Euler characteristics and establish…