2 citations · 2 across the 7 of their papers we have counts for
9 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…
Characterization of Trees with Maximum Security
Alex S. A. Alochukwu, Audace A. V. Dossou-Olory, Fadekemi J. Osaye +5
The rank (also known as protection number or leaf-height) of a vertex in a rooted tree is the minimum distance between the vertex and any of its leaf descendants. We consider the s…
Positive-Definite Matrices over Finite Fields
Joshua Cooper, Erin Hanna, Hays Whitlatch
The study of positive-definite matrices has focused on Hermitian matrices, that is, square matrices with complex (or real) entries that are equal to their own conjugate transposes.…
Counting Power Domination Sets in Complete m-ary Trees
Sviatlana Kniahnitskaya, Michele Ortiz, Olivia Ramirez +2
Motivated by the question of computing the probability of successful power domination by placing k monitors uniformly at random, in this paper we give a recursive formula to count…
On the Number of Cholesky Roots of the Zero Matrix over F2
Hays Whitlatch
A square, upper-triangular matrix U is a Cholesky root of a matrix M provided U*U=M, where * represents the conjugate transpose. Over finite fields, as well as over the reals, it s…
A positivity phenomenon in Elser's Gaussian-cluster percolation model
Galen Dorpalen-Barry, Cyrus Hettle, David C. Livingston +4
Veit Elser proposed a random graph model for percolation in which physical dimension appears as a parameter. Studying this model combinatorially leads naturally to the consideratio…
A New Characterization of -Posets
Joshua Cooper, Peter Gartland, Hays Whitlatch
In 2016, Hasebe and Tsujie gave a recursive characterization of the set of induced -free and bowtie-free posets; Misanantenaina and Wagner studied these orders further, naming t…
Analogies between the crossing number and the tangle crossing number
Robin Anderson, Shuliang Bai, Fidel Barrera-Cruz +8
Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of…
Uniquely Pressable Graphs: Characterization, Enumeration, and Recognition
Joshua N. Cooper, Hays W. Whitlatch
We consider "pressing sequences", a certain kind of transformation of graphs with loops into empty graphs, motivated by an application in phylogenetics. In particular, we address t…