Related papers: Difference Sets with Few Character Values
Understanding accent is an issue which can derail any human-machine interaction. Accent classification makes this task easier by identifying the accent being spoken by a person so that the correct words being spoken can be identified by…
We construct a new family of homomorphisms from Specht modules into Foulkes modules for the symmetric group. These homomorphisms are used to give a combinatorial description of the minimal partitions (in the dominance order) which label…
Scientific expertise often requires recognizing subtle visual differences that remain challenging to articulate even for domain experts. We present a system that leverages generative models to automatically discover and visualize minimal…
What makes sets, or more precisely, the category {\bf Set} important in Mathematics are the well known {\it two} specific ways in which arbitrary mappings $f : X \longrightarrow Y$ between any two sets $X, Y$ can {\it fail} to be…
In the paper we study properties of the set of critical points for self-similar sets. We introduce simple condition that implies at most countably many critical values and we construct a self-similar set with uncountable set of critical…
Character polynomials are used to study the restriction of a polynomial representation of a general linear group to its subgroup of permutation matrices. A simple formula is obtained for computing inner products of class functions given by…
We present some variations on some of the main open problems on character degrees. We collect some of the methods that have proven to be very useful to work on these problems. These methods are also useful to solve certain problems on zeros…
We investigate properties of families $F$ of subsets of a finite set in a situation where subsets are incomparable by the binary inclusion relation and a) for any $A\notin F$, there is such set $A'\in F$ that either $A\subset A'$ or…
Explaining decisions of black-box classifiers is both important and computationally challenging. In this paper, we scrutinize explainers that generate feature-based explanations from samples or datasets. We start by presenting a set of…
Identifying differences between groups is one of the most important knowledge discovery problems. The procedure, also known as contrast sets mining, is applied in a wide range of areas like medicine, industry, or economics. In the paper we…
We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations defined from a suitable filtration of the Weyl algebra $A_{n}(k)$. This generalizes an important…
We classify the discriminantly separable polynomials of degree two in each of three variables, defined by a property that all the discriminants as polynomials of two variables are factorized as products of two polynomials of one variable…
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
This paper proposes a method to use deep neural networks as end-to-end open-set classifiers. It is based on intra-class data splitting. In open-set recognition, only samples from a limited number of known classes are available for training.…
Frame difference families, which can be obtained via a careful use of cyclotomic conditions attached to strong difference families, play an important role in direct constructions for resolvable balanced incomplete block designs. We…
Distributional shift between domains poses great challenges to modern machine learning algorithms. The domain generalization (DG) signifies a popular line targeting this issue, where these methods intend to uncover universal patterns across…
A notion of gcd chain has been introduced by the author at ISSAC 2017 for two univariate monic polynomials with coefficients in a ring R = k[x_1, ..., x_n ]/(T) where T is a primary triangular set of dimension zero. A complete algorithm to…
Let $G$ be a finite group, and let ${\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. Define then the character degree graph $\Delta(G)$ as the (simple undirected) graph whose vertices are the prime…
We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t. We prove the first nontrivial degree formula and use it to show that…
There are characteristic classes that are the obstructions to the vanishing of the differentials in the Lyndon-Hochischild-Serre spectral sequence of an extension of an integral lattice L by a group G. These characteristic classes exist in…