2 papers
math.CO2025
A New Formula for the Determinant and Bounds on Its Tensor and Waring Ranks
Robin Houston, Adam P. Goucher, Nathaniel Johnston
We present a new explicit formula for the determinant that contains superexponentially fewer terms than the usual Leibniz formula. As an immediate corollary of our formula, we show…
math.CO2024
Laplacian - and -diagonalizable graphs
Nathaniel Johnston, Sarah Plosker
A graph is called "Laplacian integral" if the eigenvalues of its Laplacian matrix are all integers. We investigate the subset of these graphs whose Laplacian is furthermore diagona…