Joseph E. Bonin

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20242026

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math.CO2026

Free products, extremal matroids, and a generalization of perfect matroid designs

Joseph E. Bonin

Extremal matroids are those that yield vertices in the polytope of matroids. We show how to get the point, in the appropriate polytope of matroids, for the free product $M\square M…

math.CO2025

A construction that preserves the configuration of a matroid, with applications to lattice path matroids

Joseph E. Bonin, Anna de Mier

The configuration of a matroid $M$ is the abstract lattice of cyclic flats (flats that are unions of circuits) where we record the size and rank of each cyclic flat, but not the se…

math.CO2025

The $G$ -invariant and catenary data of a matroid

Joseph E. Bonin, Joseph P. S. Kung

The catenary data of a matroid $M$ of rank $r$ on $n$ elements is the vector $(I^½ (M; a_{0}, a_{1}, \dots, a_{r}))$ , indexed by compositions $(a_{0}, a_{1}, \dots, a_{r})$ , where $a_{0} \geq 0$ ,\, $a_…

math.CO2024

A characterization of positroids, with applications to amalgams and excluded minors

Joseph E. Bonin

A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over $R$ , each $r$ by $r$ submatrix of which has nonnegative determ…

Free products, extremal matroids, and a generalization of perfect matroid designs

A construction that preserves the configuration of a matroid, with applications to lattice path matroids

The G-invariant and catenary data of a matroid

A characterization of positroids, with applications to amalgams and excluded minors

The $G$ -invariant and catenary data of a matroid