3 papers
math.CO2022
Homogeneous Sets in Graphs and a Chromatic Multisymmetric Function
Logan Crew, Evan Haithcock, Josephine Reynes +1
In this paper, we extend the chromatic symmetric function to a chromatic -multisymmetric function , defined for graphs equipped with a partition of their vertex set int…
math.CO2021
The Determinant of -Matrices and Oriented Hypergraphs
Lucas J. Rusnak, Josephine Reynes, Russell Li +2
The determinants of -matrices are calculated by via the oriented hypergraphic Laplacian and summing over an incidence generalization of vertex cycle-covers. These cycle-…
math.CO2020
Generalizing Kirchhoff laws for Signed Graphs
Lucas J. Rusnak, Josephine Reynes, Skyler J. Johnson +1
Kirchhoff-type Laws for signed graphs are characterized by generalizing transpedances through the incidence-oriented structure of bidirected graphs. The classical -arborescence…