M. Barry

activity

20112026

most citedMore on Periodicity and Duality associated with Jordan partitions

1 citations · 1 across the 7 of their papers we have counts for

collaborators

9 papers

math.RT2026

Generators for Tensor Product Components

Michael J. J. Barry

Let $p$ be a prime number, $F$ a field of characteristic $p$ , and $G$ a cyclic group of order $q = p^{a}$ for some positive integer $a$ . Under these circumstances every indecomposable…

math.CO2022

An application of sums of triple products of binomials

Michael J. J. Barry

We prove that a certain family of sums of products of three binomials has alternating behavior modulo a prime $p$ . To accomplish this we rewrite these sums as signed sums of produc…

math.RT2022

Generators for Decompositions of Tensor Products of Indecomposable Modules

Michael J. J. Barry

Let $F$ be a field of non-zero characteristic $p$ , let $G$ be a cyclic group of order $q = p^{a}$ for some positive integer $a$ , and let $U$ and $W$ be indecomposable $F G$ -modules. W…

math.CO2020

Set Equality in Combinatorial Game Theory

Michael J. J. Barry

In Combinatorial Game Theory, the fundamental relation of game equivalence, denoted by $=$ , is introduced early on and overrides the notion of set equality. We explore what happens…

math.RT2019★ 1 cited

More on Periodicity and Duality associated with Jordan partitions

Michael J. J. Barry

Let $J_{r}$ denote a full $r \times r$ Jordan block matrix with eigenvalue $1$ over a field $F$ of characteristic $p$ . For positive integers $r$ and $s$ with $r \leq s$ , the Jordan c…

math.GR2015

Generators for Decompositions of Tensor Products of Modules associated with standard Jordan partitions

Michael J. J. Barry

If $K$ is a field of finite characteristic $p$ , $G$ is a cyclic group of order $q = p^{α}$ , $U$ and $W$ are indecomposable $K G$ -modules with $dim U = m$ and $dim W = n$ , and $λ (m, n, p)$ i…

math.GR2014

On a Question of Glasby, Praeger, and Xia in Characteristic $2$

Michael J. J. Barry

Recently, Glasby, Praeger, and Xia asked for necessary and sufficient conditions for the `Jordan partition' $λ (m, n, p)$ to be standard. Previously we gave such conditions when $p$ i…

math.GR2014

On a Question of Glasby, Praeger, and Xia

Michael J. J. Barry

Recently, Glasby, Praeger, and Xia asked for necessary and sufficient conditions for the `Jordan Partition' $λ (r, s, p)$ to be standard. We give such conditions when $p$ is an odd pr…

math.GR2011

On Conditions Relating to Nonsolvability

Michael J. J. Barry

Recent work of Kaplan and Levy refining a nonsolvability criterion proved by Thompson in his N-Groups paper prompts questions on whether certain conditions on groups are equivalent…

Generators for Tensor Product Components

An application of sums of triple products of binomials

Generators for Decompositions of Tensor Products of Indecomposable Modules

Set Equality in Combinatorial Game Theory

More on Periodicity and Duality associated with Jordan partitions

Generators for Decompositions of Tensor Products of Modules associated with standard Jordan partitions

On a Question of Glasby, Praeger, and Xia in Characteristic 2

On a Question of Glasby, Praeger, and Xia

On Conditions Relating to Nonsolvability

On a Question of Glasby, Praeger, and Xia in Characteristic $2$