Related papers: Character table sudokus

In this paper we provide three new results axiomatizing the core of games in characteristic function form (not necessarily having transferable utility) obeying an innocuous condition (that the set of individually rational pay-off vectors is…

Sudoku is a puzzle well-known to the scientific community with simple rules of completion, which may require a com-plex line of reasoning. This paper addresses the problem of partitioning the Sudoku image into a 1-D array, recognizing…

Berkovich, Chillag and Herzog characterized all finite groups $G$ in which all the nonlinear irreducible characters of $G$ have distinct degrees. In this paper we extend this result showing that a similar characterization holds for all…

The success of Large Language Models (LLMs) in human-AI collaborative decision-making hinges on their ability to provide trustworthy, gradual, and tailored explanations. Solving complex puzzles, such as Sudoku, offers a canonical example of…

The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the…

We describe a translation from a fragment of SUMO (SUMO-K) into higher-order set theory. The translation provides a formal semantics for portions of SUMO which are beyond first-order and which have previously only had an informal…

It is known that, if all the real-valued irreducible characters of a finite group have odd degree, then the group has normal Sylow $2$-subgroup. We generalize this result for Sylow $p$-subgroups, for any prime number $p$, while assuming the…

we obtain a necessary condition for the character degree graph with all of its vertices are odd degree of a finite solvable group G.

Odlyzko and Stanley introduced a greedy algorithm for constructing infinite sequences with no 3-term arithmetic progressions when beginning with a finite set with no 3-term arithmetic progressions. The sequences constructed from this…

Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…

Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and…

In this paper, we present a new method to construct solvable groups with derived length four and four character degrees. We then use this method to present a number of new families of groups with derived length four and four character…

Characters are integral to long-form narratives, but are poorly understood by existing story analysis and generation systems. While prior work has simplified characters via graph-based methods and brief character descriptions, we aim to…

We define the position of an irreducible complex character of a finite group as an alternative to the degree. We then use this to define three classes of groups: PR-groups, IPR-groups and weak IPR-groups. We show that IPR-groups and weak…

We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a ``rigidity'' approach. The way we use to…

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups $\text{SL}_{2}(q)$ for $q$ even, over a large enough field $k$ of positive characteristic…

Let X,Y be finite sets and T a set of functions from X -> Y which we will call "tableaux". We define a simplicial complex whose facets, all of the same dimension, correspond to these tableaux. Such "tableau complexes" have many nice…

We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and…

A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…