S. McGuinness

activity

20192026

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6 papers · 1 filter

math.CO2026

Short Rainbow Circuits in Regular Matroids

Sean McGuinness

DeVos et al conjectured that if $M$ is a simple, regular matroid and $c$ is a colouring of the elements of $M$ with $r (M) + 1$ colours, where each colour class has at least two eleme…

math.CO2024

Skew circuits and circumference in a binary matroid

Sean McGuinness

Let C_1 and C_2 be skew circuits in a binary matroid having circumference c. For any positive integer k there is a constant a_k such that if min { |A| ; C_1 \subset A \subset E-A}…

math.CO2023

Cyclic Orderings of Paving Matroids

Sean McGuinness

A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miy…

math.CO2023

Serial Exchanges in Random Bases

Sean McGuinness

It was conjectured by Kotlar and Ziv that for any two bases $B_{1}$ and $B_{2}$ in a matroid $M$ and any subset $X \subset B_{1}$ , there is a subset $Y$ and orderings $x_1 \prec x_2 \pre…

math.CO2019

Frame Matroids, Toric Ideals, and a Conjecture of White

Sean McGuinness

Blasiak verified a conjecture of White for graphic matroids by showing that the toric ideal of a graphic matroid is generated by quadrics. In this paper, we extend this result to f…

math.CO2019

Girth conditions and Rota's basis conjecture

Benjamin Friedman, Sean McGuinness

Rota's basis conjecture (RBC) states that given a collection $B$ of $n$ bases in a matroid $M$ of rank $n$ , one can always find $n$ disjoint rainbow bases with respect to…