100 citations · 310 across the 26 of their papers we have counts for
26 papers
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…
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 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…
Connectivity gaps among matroids with the same enumerative invariants
Joseph E. Bonin, Kevin Long
Many important enumerative invariants of a matroid can be obtained from its Tutte polynomial, and many more are determined by two stronger invariants, the -invariant a…
A characterization of positroids, with applications to amalgams and excluded minors
Joseph E. Bonin
A matroid of rank on elements is a positroid if it has a representation by an by matrix over , each by submatrix of which has nonnegative determ…
The excluded minors for three classes of 2-polymatroids having special types of natural matroids
Joseph E. Bonin, Kevin Long
If is a minor-closed class of matroids, the class of integer polymatroids whose natural matroids are in is also minor closed, as is the c…
The natural matroid of an integer polymatroid
Joseph E. Bonin, Carolyn Chun, Tara Fife
The natural matroid of an integer polymatroid was introduced to show that a simple construction of integer polymatroids from matroids yields all integer polymatroids. As we illustr…
The excluded minors for lattice path polymatroids
Joseph Bonin, Carolyn Chun, Tara Fife
We find the excluded minors for the minor-closed class of lattice path polymatroids as a subclass of the minor-closed class of Boolean polymatroids. Like lattice path matroids and…
Matroids with different configurations and the same -invariant
Joseph E. Bonin
From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied ma…
The free -cone of a matroid and its -invariant
Joseph E. Bonin, Kevin Long
For a matroid , its configuration determines its -invariant. Few examples are known of pairs of matroids with the same -invariant but different configu…
Decomposable polymatroids and connections with graph coloring
Joseph E. Bonin, Carolyn Chun
We introduce ideas that complement the many known connections between polymatroids and graph coloring. Given a hypergraph that satisfies certain conditions, we construct polymatroi…
Delta-matroids as subsystems of sequences of Higgs lifts
Joseph E Bonin, Carolyn Chun, Steven D Noble
In her paper "Generalized matroids and supermodular colourings", Tardos studied special delta-matroids obtained from sequences of Higgs lifts; these are the full Higgs lift delta-m…
The -invariant and catenary data of a matroid
Joseph E. Bonin, Joseph P. S. Kung
The catenary data of a matroid of rank on elements is the vector , indexed by compositions , where ,\, $a_i…
Lattices related to extensions of presentations of transversal matroids
Joseph E. Bonin
For a presentation of a transversal matroid , we study the set of single-element transversal extensions of that have presentations that exten…
An infinite family of excluded minors for strong base-orderability
Joseph E. Bonin, Thomas J. Savitsky
We discuss a conjecture of Ingleton on excluded minors for base-orderability, and, extending a result he stated, we prove that infinitely many of the matroids that he identified ar…
Semidirect sums of matroids
Joseph E. Bonin, Joseph P. S. Kung
For matroids M and N on disjoint sets S and T, a semidirect sum of M and N is a matroid K on the union of S and T that, like the direct sum and the free product, has the restrictio…
Sparse paving matroids, basis-exchange properties, and cyclic flats
Joseph E. Bonin
We provide evidence for five long-standing, basis-exchange conjectures for matroids by proving them for the enormous class of sparse paving matroids. We also explore the role that…
Characterizations of transversal and fundamental transversal matroids
Joseph E. Bonin, Joseph P. S. Kung, Anna de Mier
A result of Mason, as refined by Ingleton, characterizes transversal matroids as the matroids that satisfy a set of inequalities that relate the ranks of intersections and unions o…
A construction of infinite sets of intertwines for pairs of matroids
Joseph E. Bonin
An intertwine of a pair of matroids is a matroid such that it, but none of its proper minors, has minors that are isomorphic to each matroid in the pair. For pairs for which neithe…
Lattice path matroids: the excluded minors
Joseph E. Bonin
A lattice path matroid is a transversal matroid for which some collection of incomparable intervals in some linear order on the ground set is a presentation. We characterize the mi…
A Note on the Sticky Matroid Conjecture
Joseph E. Bonin
A matroid is sticky if any two of its extensions by disjoint sets can be glued together along the common restriction (that is, they have an amalgam). The sticky matroid conjecture…
Splicing Matroids
Joseph E. Bonin, William R. Schmitt
We introduce and study a natural variant of matroid amalgams. For matroids M(A) and N(B) such that M/(A-B)=N(B-A), we define a splice of M and N to be a matroid L on the union of A…
Transversal Lattices
Joseph E. Bonin
A flat of a matroid is cyclic if it is a union of circuits; such flats form a lattice under inclusion and, up to isomorphism, all lattices can be obtained this way. A lattice is a…
The Lattice of Cyclic Flats of a Matroid
Joseph E. Bonin, Anna de Mier
A flat of a matroid is cyclic if it is a union of circuits. The cyclic flats of a matroid form a lattice under inclusion. We study these lattices and explore matroids from the pers…
Multi-Path Matroids
Joseph E. Bonin, Omer Gimenez
We introduce the minor-closed, dual-closed class of multi-path matroids. We give a polynomial-time algorithm for computing the Tutte polynomial of a multi-path matroid, we describe…