B. Rhoades

collaborators

9 papers

math.CO2026

Derangement permutation matrices and orbit harmonics

Yupeng Li, Jasper Liu, Brendon Rhoades

The paper investigates the algebraic and representation-theoretic properties of the set of derangement permutation matrices via the orbit harmonics quotient ring, giving explicit g…

math.CO2026

Superspace coinvariants for wreath products

Sutanay Bhattacharya, Brendon Rhoades

Let $I^c ◯$ be the superspace ring of regular differential forms on the affine space $C^{n}$ . If $G \subseteq G L_{n} (C)$ is a complex reflection group, the {\em $G$ -supe…

math.CO2026

Superspace coinvariants and inverse systems for $G L_{n} (F_{q})$

Brendon Rhoades, Andy Wilson

Let $q$ be a prime power and write $I^c ◯$ for the bigraded algebra of regular differential forms over $F_{q}^{n}$ . The general linear group $G L_{n} (F_{q})$ acts on $I^c ◯$ ; wr…

math.CO2026

Big Varchenko-Gelfand rings and orbit harmonics

Brendon Rhoades

Let $M$ be a conditional oriented matroid. We define a graded algebra $VG_{M}$ with vector space dimension given by the number of covectors in…

math.CO2026

Superspace coinvariants and hyperplane arrangements

Robert Angarone, Patricia Commins, Trevor Karn +2

Let $I^c ◯$ be the {\em superspace ring} of polynomial-valued differential forms on affine $n$ -space. The natural action of the symmetric group $S_{n}$ on $n$ -space induces a…

math.CO2025

A proof of the Fields Conjectures

Satoshi Murai, Brendon Rhoades, Andy Wilson

The {\em superspace ring} of rank $n$ is the algebra $I^c ◯_{n}$ of differential forms on affine $n$ -space. The algebra $I^c ◯_{n}$ is bigraded with respect to polynomial and exterior degree…

Derangement permutation matrices and orbit harmonics

Superspace coinvariants for wreath products

Superspace coinvariants and inverse systems for GLn​(Fq​)

Big Varchenko-Gelfand rings and orbit harmonics

Superspace coinvariants and hyperplane arrangements

A proof of the Fields Conjectures

Superspace coinvariants and inverse systems for $G L_{n} (F_{q})$