4 papers
The effect of edge deletion on noncommutative distances on graphs
Eric Swartz
For a Dirac operator on a finite weighted graph, let denote the associated noncommutative (Connes) distance. We show that deleting an edge can actually decrease the nonco…
Enumerating Vector Parking Functions and their Outcomes Based on Specified Lucky Cars
Melanie Ferreri, Pamela E. Harris, Lucy Martinez +1
In a parking function, a car is considered lucky if it is able to park in its preferred spot. Extending work of Harris and Martinez, we enumerate outcomes of parking functions with…
Noncommutative distances on graphs: An explicit approach via Birkhoff-James orthogonality
Pierre Clare, Chi-Kwong Li, Edward Poon +1
We study the problem of calculating noncommutative distances on graphs, using techniques from linear algebra, specifically, Birkhoff-James orthogonality. A complete characterizatio…
Combinatorial transfer: a new method for constructing infinite families of nonabelian difference sets, partial difference sets, and relative difference sets
Eric Swartz, James A. Davis, John Polhill +1
For nearly a century, mathematicians have been developing techniques for constructing abelian automorphism groups of combinatorial objects, and, conversely, constructing combinator…