Kristin Heysse

collaborators

4 papers

math.CO2026

(32-1)-Avoiding Permutations with Maximum Inversion Number

Andrew Beveridge, Kristin Heysse, Paige Robertson

A permutation $I ¨ \in S_{n}$ is (32-1)-avoiding when there do not exist $1 \leq i < i + 1 < j \leq n$ such that $I ¨ _{i} > I ¨ _{i + 1} > I ¨ _{j}$ . We determine the maximum inversion number for (…

math.CO2025

Chip-Firing Games on Banana Trees

Marchelle Beougher, Nila Cibu, Kexin Ding +6

We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomia…

math.CO2025

The Exact Mixing Time for Trees with Fixed Diameter

Andrew Beveridge, Kristin Heysse, Rhys O'Higgins +1

We characterize the extremal structure for the exact mixing time for random walks on trees $T_{n, d}$ of order $n$ with diameter $d$ . Given a graph $G = (V, E)$ , let $H (v, I ¨ )$ denote t…

math.CO2024

Defective eigenvalues of the non-backtracking matrix

Kristin Heysse, Kate Lorenzen, Carolyn Reinhart

We consider graphs for which the non-backtracking matrix has defective eigenvalues, or graphs for which the matrix does not have a full set of eigenvectors. The existence of these…