Gregory J. Clark

activity

20172021

collaborators

3 papers

math.CO2021

Applications of the Harary-Sachs Theorem for Hypergraphs

Gregory J. Clark, Joshua Cooper

The Harary-Sachs theorem for $k$ -uniform hypergraphs equates the codegree- $d$ coefficient of the adjacency characteristic polynomial of a uniform hypergraph with a weighted sum of…

math.CO2018

Leading Coefficients and the Multiplicity of Known Roots

Gregory J. Clark, Joshua N. Cooper

We show that a monic univariate polynomial over a field of characteristic zero, with $k$ distinct non-zero known roots, is determined by its $k$ proper leading coefficients by prov…

math.SP2017

On the Adjacency Spectra of Hypertrees

Gregory J. Clark, Joshua Cooper

We extend the results of Zhang et al. to show that $λ$ is an eigenvalue of a $k$ -uniform hypertree $(k \geq 3)$ if and only if it is a root of a particular matching polynomial for…