Related papers: Character Levels and Character Bounds

Social media messages' brevity and unconventional spelling pose a challenge to language identification. We introduce a hierarchical model that learns character and contextualized word-level representations for language identification. Our…

If all of the entries of a large $S_n$ character table are covered up and you are allowed to uncover one entry at a time, then how can you quickly identify all of the indexing characters and conjugacy classes? We present a fast algorithmic…

A character of a group is said to be super-monomial if every primitive character inducing it is linear. It is conjectured by Isaacs that every irreducible character of an odd $M$-group is super-monomial. We show that all non linear…

We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different…

This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's…

We investigate the finite groups $G$ for which $\chi(1)^{2}=|G:Z(\chi)|$ for all characters $\chi \in Irr(G)$ and $|cd(G)|=2$, where $cd(G)=\{\chi(1)| \chi \in Irr(G)\}$. We call such a group a GVZ-group with two character degrees. We…

We establish character rigidity for all non-uniform higher-rank irreducible lattices in semisimple groups of characteristic other than 2. This implies stabilizer rigidity for probability measure preserving actions and rigidity of invariant…

This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose…

We introduce the concept of regular expression characteristics as a unified way to concisely express bounds on time-series constraints. This allows us not only to define time-series constraints in a compositional way, but also to deal with…

In this paper, we determine new characterizations of nested and nested GVZ-groups, including character-free characterizations, but we additionally show that nested groups and nested GVZ-groups can be defined in terms of the existence of…

The proof of the inductive McKay condition has been shown to imply that the character theory above the characters of degree not divisible by $p$ of a normal subgroup is locally determined. In this note, we establish a similar result for the…

A classical theorem of John Thompson on character degrees asserts that if the degree of every ordinary irreducible character of a finite group $G$ is 1 or divisible by a prime $p$, then $G$ has a normal $p$-complement. We obtain a…

For families of all theories of arbitrary given languages we describe ranks and degrees. In particular, we characterize (non-)totally transcendental families. We apply these characterizations for the families of all theories of given…

In 1961, Solomon gave upper and lower bounds for the sum of all the entries in the character table of a finite group in terms of elementary properties of the group. In a different direction, we consider the ratio of the character table sum…

We prove that if the average of the degrees of the irreducible characters of a finite group $G$ is less than 16/5, then $G$ is solvable. This solves a conjecture of I.M. Isaacs, M. Loukaki, and the first author. We discuss related…

The present work deals with the characterization of parity vectors of Collatz sequences (of finite and infinite length). Such a characterization leads to the determination of several numbers (integers or non-integers) that we call the…

Stanley and Odlyzko proposed a method for greedily constructing sets with no 3-term arithmetic progressions. It is conjectured that there is a dichotomy between such sequences: those that have a periodic structure as the sequence satisfies…

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical…

We prove the existence of a limit shape and give its explicit description for certain probability distribution on signatures (or highest weights for unitary groups). The distributions have representation theoretic origin-they encode…

We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of…