Search Results - "Bonin, Joseph E."

The Free m-Cone of a Matroid and Its G-Invariant by Bonin, Joseph E., Long, Kevin

“…For a matroid, its configuration determines its G -invariant. Few examples are known of pairs of matroids with the same G -invariant but different…”
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Basis-exchange properties of sparse paving matroids by Bonin, Joseph E.

“…It has been conjectured that, asymptotically, almost all matroids are sparse paving matroids. We provide evidence for five long-standing, basis-exchange…”
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Characterizations of PG(n − 1, q)\PG(k − 1, q) by Numerical and Polynomial Invariants by Ankney, Rachelle M., Bonin, Joseph E.

“…We show that the simple matroid PG(n−1,q)\PG(k−1,q), for n≥4 and 1≤k≤n−2, is characterized by a variety of numerical and polynomial invariants. In particular,…”
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Splicing matroids by Bonin, Joseph E., Schmitt, William R.

“…We introduce and study a natural variant of matroid amalgams. For matroids M ( A ) and N ( B ) with M . ( A ∩ B ) = N | ( A ∩ B ) , we define a splice of M and…”
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A characterization of positroids, with applications to amalgams and excluded minors by Bonin, Joseph E.

“…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…”
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Amalgams of extremal matroids with no U2,ℓ+2-minor by BONIN, Joseph E, RONG CHEN, XIANG, Kai-Nan

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Extending a matroid by a cocircuit by Bonin, Joseph E.

“…Our main result describes how to extend a matroid so that its ground set is a modular hyperplane of the larger matroid. This result yields a new way to view…”
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Matroids with different configurations and the same G-invariant by Bonin, Joseph E.

“…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…”
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Connectivity gaps among matroids with the same enumerative invariants by Bonin, Joseph E., Long, Kevin

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The Free m-Cone of a Matroid and Its $${\mathcal {G}}$$-Invariant by Bonin, Joseph E., Long, Kevin

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Lattices Related to Extensions of Presentations of Transversal Matroids by Bonin, Joseph E.

“…For a presentation $\mathcal{A}$ of a transversal matroid $M$, we study the ordered set $T_{\mathcal{A}}$ of single-element transversal extensions of $M$ that…”
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Lattice path matroids: The excluded minors by Bonin, Joseph E.

“…A lattice path matroid is a transversal matroid for which some antichain of intervals in some linear order on the ground set is a presentation. We characterize…”
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Delta-matroids as subsystems of sequences of Higgs lifts by Bonin, Joseph E., Chun, Carolyn, Noble, Steven D.

“…In [30], Tardos studied special delta-matroids obtained from sequences of Higgs lifts; these are the full Higgs lift delta-matroids that we treat and around…”
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An infinite family of excluded minors for strong base-orderability by Bonin, Joseph E., Savitsky, Thomas J.

“…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…”
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The excluded 3-minors for vf-safe delta-matroids by Bonin, Joseph E., Chun, Carolyn, Noble, Steven D.

“…Vf-safe delta-matroids have the desirable property of behaving well under certain duality operations. Several important classes of delta-matroids are known to…”
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Tutte polynomials of q-cones by E. Bonin, Joseph, Qin, Hongxun

“…We derive a formula for the Tutte polynomial t( G′; x, y) of a q-cone G′ of a GF( q)-representable geometry G in terms of t( G; x, y). We use this to construct…”
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A Note on the Sticky Matroid Conjecture by Bonin, Joseph E.

“…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…”
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A characterization of positroids, with applications to amalgams and excluded minors by Bonin, Joseph E

“…European Journal of Combinatorics, 2024 A matroid of rank $r$ on $n$ elements is a positroid if it has a representation by an $r$ by $n$ matrix over…”
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The Lattice of Cyclic Flats of a Matroid by Bonin, Joseph E., de Mier, Anna

“… 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…”
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Extensions and presentations of transversal matroids by Bonin, Joseph E., de Mier, Anna

“…A transversal matroid M can be represented by a collection of sets, called a presentation of M, whose partial transversals are the independent sets of M…”
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