7 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…
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…
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…