6 papers · 1 filter
Counting Cholesky factorizations of the zero matrix over
Joshua Cooper, Hays Whitlatch
A square, upper-triangular matrix is a Cholesky root of a matrix provided , where represents the conjugate transpose when working over the complex field a…
Multigraphs with Unique Partition into Cycles
Joshua Cooper, Utku Okur
Due to Veblen's Theorem, if a connected multigraph has even degrees at each vertex, then it is Eulerian and its edge set has a partition into cycles. In this paper, we show tha…
Partitions of an Eulerian Digraph into Circuits
Joshua Cooper, Utku Okur
We investigate a cancellation property satisfied by a connected Eulerian digraph . Namely, unless is a single directed cycle, we have , whe…
Permutations minimizing the number of collinear triples
Joshua Cooper, Jack Hyatt
We characterize the permutations of whose graph minimizes the number of collinear triples and describe the lexicographically-least one, affirming a conjecture of Coo…
Characteristic Polynomials and Hypergraph Generating Functions via Heaps of Pieces
Joshua Cooper, Krystal Guo, Utku Okur
It is a classical result due to Jacobi in algebraic combinatorics that the generating function of closed walks at a vertex in a graph is determined by the rational function…
Polynomial Reconstruction Problem for Hypergraphs
Joshua Cooper, Utku Okur
We show that, in general, the characteristic polynomial of a hypergraph is not determined by its ``polynomial deck'', the multiset of characteristic polynomials of its vertex-delet…