Luke Pebody

activity

20142024

most citedExtension of a Method of Gilmer

1 citations · 1 across the 7 of their papers we have counts for

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6 papers · 1 filter

math.CO2024

Nordhaus-Gaddum inequalities for the number of cliques in a graph

Deepak Bal, Jonathan Cutler, Luke Pebody

Nordhaus and Gaddum proved sharp upper and lower bounds on the sum and product of the chromatic number of a graph and its complement. Over the years, similar inequalities have been…

math.CO2024

Sums, Differences and Dilates

Jonathan Cutler, Luke Pebody, Amites Sarkar

Given a set of integers $A$ and an integer $k$ , write $A + k \cdot A$ for the set ${a + k b : a \in A, b \in A}$ . Hanson and Petridis showed that if $∣ A + A ∣ \leq K ∣ A ∣$ then $|A+2\cdot A|\le K^…

math.CO2022★ 1 cited

Extension of a Method of Gilmer

Luke Pebody

It is a well-known conjecture, sometimes attributed to Frankl, that for any family of sets which is closed under the union operation, there is some element which is contained in at…

math.CO2021

Minimum degrees of finite rectangular bands, null semigroups, and variants of full transformation semigroups

Peter J Cameron, James East, Des FitzGerald +3

For a positive integer $n$ , the full transformation semigroup $T_{n}$ consists of all self maps of the set ${1, \dots, n}$ under composition. Any finite semigroup $S$ embeds in some…

math.CO2016

Set Reconstruction on the Hypercube

Luke Pebody

Given an action of a group $G$ on a set $S$ , the $k$ -deck of a subset $T$ of $S$ is the multiset of all subsets of $T$ of size $k$ , each given up to translation by $G$ . For a given…

math.CO2014

Maximal-clique partitions and the Roller Coaster Conjecture

Jonathan Cutler, Luke Pebody

A graph $G$ is {\em well-covered} if every maximal independent set has the same cardinality $q$ . Let $i_{k} (G)$ denote the number of independent sets of cardinality $k$ in $G$ . Brown…