11 citations · 24 across the 9 of their papers we have counts for
10 papers
Algebraic Properties of a Hypergraph Lifting Map
Mark Budden, Josh Hiller, Tommy Meek +1
Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain -uniform hypergraph to a given graph, bounding cliques in a pr…
Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles
W. Zane Billings, Justin Clifton, Josh Hiller +6
We present a recursive formula for the number of ways to color vertices blue in an r-uniform hyperpath of size while avoiding a blue monochromatic sub-hyperpath of length k…
Constructive Methods in Gallai-Ramsey Theory for Hypergraphs
Mark Budden, Joshua Hiller, Andrew Penland
Much recent progress in hypergraph Ramsey theory has focused on constructions that lead to lower bounds for the corresponding Ramsey numbers. In this paper, we consider application…
Minimally Connected Hypergraphs
Mark Budden, Josh Hiller, Andrew Penland
Graphs and hypergraphs are foundational structures in discrete mathematics. They have many practical applications, including the rapidly developing field of bioinformatics, and mor…
On Covers of Dihedral 2-Groups by Powerful Subgroups
Risto Atanasov, Adam Gregory, Luke Guatelli +1
A finite -group is called \textit{powerful} if either is odd and or and . A {\em{cover}} for a group is a collection of su…
Trees and -Good Hypergraphs
Mark Budden, Andrew Penland
Trees fill many extremal roles in graph theory, being minimally connected and serving a critical role in the definition of -good graphs. In this article, we consider the general…
Nearly Maximal Hausdorff Dimension in Finitely Constrained Groups
Andrew Penland
This work continues the study of the properties of finitely constrained groups of binary tree automorphisms in terms of their Hausdorff dimension. We prove that there are exactly $…
A Language Hierarchy and Kitchens-Type Theorem for Self-Similar Groups
Andrew Penland, Zoran Šunić
We generalize the notion of self-similar groups of infinite tree automorphisms to allow for groups which are defined on a tree but do not act faithfully on it. The elements of such…
Periodic Points on Shifts of Finite Type and Commensurability Invariants of Groups
David Carroll, Andrew Penland
We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, we…
Finitely constrained groups of maximal Hausdorff dimension
Andrew Penland, Zoran Sunic
We prove that if G_P is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group P of pa…