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- National Radio Astronomy ObservatoryUS83 papers
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5 papers · 2 filters
Proofs and generalizations of a homomesy conjecture of Propp and Roby
Jonathan Bloom, Oliver Pechenik, Dan Saracino
Let be a group acting on a set of combinatorial objects, with finite orbits, and consider a statistic . Propp and Roby defined the triple t…
The transition matroid of a 4-regular graph: an introduction
Lorenzo Traldi
Given a 4-regular graph , we introduce a binary matroid on the set of transitions of . Parametrized versions of the Tutte polynomial of yield several well-k…
Fixing numbers for matroids
Gary Gordon, Jennifer McNulty, Nancy Ann Neudauer
Motivated by work in graph theory, we define the fixing number for a matroid. We give upper and lower bounds for fixing numbers for a general matroid in terms of the size and maxim…
Partitions of AG(4,3) into Maximal Caps
Michael Follett, Kyle Kalail, Elizabeth McMahon +2
In a geometry, a maximal cap is a collection of points of largest size containing no lines. In AG(4,3), maximal caps contain 20 points. The 81 points of AG(4,3) can be partitioned…
Binary matroids and local complementation
Lorenzo Traldi
We introduce a binary matroid M(IAS(G)) associated with a looped simple graph G. M(IAS(G)) classifies G up to local equivalence, and determines the delta-matroid and isotropic syst…