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Linda Hoyer

Publications and source records attributed to Linda Hoyer.

5 recordsLinked to original sources
arXiv2026

On the dimensions of correlated equilibrium polytopes of generic games

In this paper, we study the dimension of the correlated equilibrium polytope of finite games. Under the oriented-matroid notion of genericity, we prove that if a generic game is not full-dimensional, then there exists a subgame whose correlated equilibrium polytope is affinely isomorphic to that of the original game. This settles and generalizes an earlier conjecture of Brandenburg, Hollering, and Portakal (2024). Moreover, we show that the existence of a correlated equilibrium whose slices are all non-zero implies that the correlated equilibrium polytope is either full-dimensional or a singleton.

math.CO↗
arXiv2024

Orthogonal Determinants of $\mathrm{GL}_n(q)$

Let $n$ be a positive integer and $q$ be a power of an odd prime. We provide explicit formulas for calculating the orthogonal determinants $\det(χ)$, where $χ\in \mathrm{Irr}(\mathrm{GL}_n(q))$ is an orthogonal character of even degree. Moreover, we show that $\det(χ)$ is "odd". This confirms a special case of a conjecture by Richard Parker.

math.RT↗
arXiv2024

On the Gram determinants of the Specht modules

For every partition $λ$ of a positive integer $n$, let $S^λ$ be the corresponding Specht module of the symmetric group $\mathfrak{S}_n$, and let $\det(λ)\in \mathbb Z$ denote the Gram determinant of the canonical bilinear form with respect to the standard basis of $S^λ$. Writing $\det(λ)=m \cdot 2^{a_λ^{(2)}}$ for integers $a_λ^{(2)}$ and $m$ with $m$ odd, we show that if the dimension of $S^λ$ is even, then $a_λ^{(2)}$ is also even. This confirms a conjecture posed by Richard Parker in the special case of the symmetric groups.

math.CO↗