Luke Pebody

collaborators

2 papers

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.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…