7 papers
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…
On the sparsity of integers in solutions to
Joshua Cooper, Joseph Preuss
We consider the Diophantine equation due to ErdÅs, where we assume . It is widely believed that there are only finitely many nontrivial solutions, and co…
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…
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…
Cryptographic Compression
Joshua Cooper, Grant Fickes
We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirabl…