Searcharxiv⌕ Search

arXiv subjects

Joseph E. Marrow

Publications and source records attributed to Joseph E. Marrow.

6 recordsLinked to original sources
arXiv2026

On Schur Rings Over Semigroups

We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two categories are provided. We prove some results for Schur rings over specific families of semigroups. We consider parallels between semigroup extensions and their Schur rings. We fully enumerate the Schur rings for all semigroups of orders 0-7, and some statistical analysis is performed.

math.GR↗
arXiv2025

Strong Gelfand pairs of the sporadic groups and their extensions

A strong Gelfand pair $(G, H)$ is a finite group $G$ and a subgroup $H$ where every irreducible character of $H$ induces to a multiplicity-free character of $G$. We determine the strong Gelfand pairs of the sporadic groups, their automorphism groups, and their covering groups. We also find the (strong) Gelfand pairs of the generalized Mathieu groups, the Tits group, and the automorphism group of the Leech Lattice.

math.RT↗
arXiv2025

The $3\times 3$ Solution to the Game of Tak

We provide answers to natural combinatorial questions which arise from learning the rules to Tak. We solve the discarded cases of the $3\times 3$ game not previously considered by Joshua Achiam, showing that Player $1$ has a forced win from any starting position, including random ones. Diagrams for both his and our solutions are provided in the hopes of making the results more accessible.

math.GM↗
arXiv2025

Strong Gelfand Pairs of the Dihedral and Dicyclic Groups

A strong Gelfand pair $(G, H)$ is a finite group $G$ and a subgroup $H$ where every irreducible character of $H$ induces to a multiplicity-free character of $G$. We determine the strong Gelfand pairs of the dihedral groups $D_{2n}$ and the dicyclic groups $Dic_{4n}$ for all $n$.

math.RT↗