arXiv subjects

Tommy Meek

Publications and source records attributed to Tommy Meek.

2 recordsLinked to original sources

arXiv2020

Algebraic Properties of a Hypergraph Lifting Map

Recent work in hypergraph Ramsey theory has involved the introduction of a "lifting map" that associates a certain $3$-uniform hypergraph to a given graph, bounding cliques in a predictable way. In this paper, we interpret the lifting map as a linear transformation. This interpretation allows us to use algebraic techniques to prove several structural properties of the lifting map, culminating in new lower bounds for certain $3$-uniform hypergraph Ramsey numbers.

math.CO↗

arXiv2020

Avoiding monochromatic sub-paths in uniform hypergraph paths and cycles

We present a recursive formula for the number of ways to color $j$ vertices blue in an r-uniform hyperpath of size $n$ while avoiding a blue monochromatic sub-hyperpath of length k. We use this result to solve the corresponding problem for $(r-1)$-tight r-uniform paths and loose r-uniform cycles. This generalizes some well known results from reliability engineering and analysis.

math.CO↗