3 papers
math.MG2020
A mélange of diameter Helly-type theorems
Travis Dillon, Pablo Soberón
A Helly-type theorem for diameter provides a bound on the diameter of the intersection of a finite family of convex sets in given some information on the diameter of…
math.NT2019
An average of generalized Dedekind sums
Travis Dillon, Stephanie Gaston
We study a generalization of the classical Dedekind sum that incorporates two Dirichlet characters and develop properties that generalize those of the classical Dedekind sum. By ca…
math.CO2018
A combinatorial interpretation of Gaussian blur
Travis Dillon
Gaussian blur is a commonly-used method to filter image data. This paper introduces the collapsing sum, a new operator on matrices that provides a combinatorial interpretation of G…