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Zero loci of nullvectors and skew zero forcing in graphs and hypergraphs
Joshua Cooper, Grant Fickes
There is interesting internal structure in the nullspaces of graph and hypergraph adjacency matrices, especially for trees, bipartite graphs, and related combinatorial classes. The…
Geometric vs Algebraic Nullity for Hyperpaths
Joshua Cooper, Grant Fickes
We consider the question of how the eigenvarieties of a hypergraph relate to the algebraic multiplicities of their corresponding eigenvalues. Specifically, we (1) fully describe th…
The Edge-Distinguishing Chromatic Number of Petal Graphs, Chorded Cycles, and Spider Graphs
Grant Fickes, Wing Hong Tony Wong
The edge-distinguishing chromatic number (EDCN) of a graph is the minimum positive integer such that there exists a vertex coloring whose induce…
Recurrence Ranks and Moment Sequences
Joshua Cooper, Grant Fickes
We introduce the "moment rank" and "unitary rank" of numerical sequences, close relatives of linear-recursive order. We show that both parameters can be characterized by a broad se…