Michael Tait

collaborators

4 papers

math.CO2025

Improved Gilbert-Varshamov bound for sum-rank-metric codes via graph theory

Aida Abiad, Harper Reijnders, Michael Tait

We use a graph-theoretic approach which yields improvements on the known Gilbert-Varshamov (GV) bound for sum-rank-metric codes for certain parameters. In particular, we show that…

math.CO2025

Improved bounds on the postage stamp problem for large numbers of stamps

Eric James Faust, Michael Tait

Let $F_{h} (n)$ denote the minimum cardinality of an additive {\em $h$ -fold basis} of ${1, 2, \dots, n}$ : a set $S$ such that any integer in ${1, 2, \dots, n}$ can be written as a su…

math.CO2025

New constructions and bounds for nonabelian Sidon sets with applications to TurÃ¡n-type problems

John Byrne, Michael Tait

An $S_{k}$ -set in a group $I^$ is a set $A \subseteq I^$ such that $I^\pm_{1} \dots I^\pm_{k} = I^_{1}^{2} \dots I^_{k}^{2}$ with $I^\pm_{i}, I^_{i}^{2} \in A$ implies $(I^\pm_{1}, \dots, I^\pm_{k}) = (I^_{1}^{2}, \dots, I^_{k}^{2})$ . An $S_{k}^{'}$ -set…

math.CO2025

Expansion in Distance Matrices

John Byrne, Jacob Johnston, Carl Schildkraut +1

The normalized distance Laplacian matrix $D^{L} (G)$ of a graph $G$ is a natural generalization of the normalized Laplacian matrix, arising from the matrix of pa…