Kai Mawhinney

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math.CO2026

Connectivity and Diameter of Friends and Strangers Graphs Using Minimum Degree

Kai Mawhinney

Given graphs $X, Y$ on $n$ vertices, Defant and Kravitz defined the friends and strangers graph, denoted $FS (X, Y)$ . The vertices of $FS (X, Y)$ are bijections $σ:V(X…

math.CO2026

Matroids with cycle systems are regular

Anton Dochtermann, Evan Huang, Kai Mawhinney +2

A cycle system for a matroid $M$ is a collection of cycles (unions of circuits) whose intersection properties mimic the cut sets of a graph. Cycle systems were introduced by Corry,…

math.CO2026

A statistic-swapping involution on the Cartesian product of the symmetric group $S_{k n}$ and the generalized symmetric group $S (k, n)$

Peter Kagey, Kai Mawhinney

We construct a statistic-swapping involution on the Cartesian product of the generalized symmetric group $S (k, n)$ with the symmetric group $S_{k n}$ , which swaps the number of fixed…

Connectivity and Diameter of Friends and Strangers Graphs Using Minimum Degree

Matroids with cycle systems are regular

A statistic-swapping involution on the Cartesian product of the symmetric group Skn​ and the generalized symmetric group S(k,n)

A statistic-swapping involution on the Cartesian product of the symmetric group $S_{k n}$ and the generalized symmetric group $S (k, n)$