48 citations · 49 across the 3 of their papers we have counts for
5 papers
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-…
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…
Oriented Hypergraphs: Balanceability
Lucas J. Rusnak, Selena Li, Brian Xu +2
An oriented hypergraph is an oriented incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and balanced matrices. We introduce hypergraphic structu…
Incidence hypergraphs: The categorical inconsistency of set-systems and a characterization of quiver exponentials
Will Grilliette, Lucas J. Rusnak
This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category of set-system hypergraphs is sho…
An Oriented Hypergraphic Approach to Algebraic Graph Theory
Nathan Reff, Lucas J. Rusnak
An oriented hypergraph is a hypergraph where each vertex-edge incidence is given a label of or . We define the adjacency, incidence and Laplacian matrices of an oriented h…