36 citations · 83 across the 30 of their papers we have counts for
37 papers
Chvátal's conjecture: a proof from The Book
David Ellis, Yuval Filmus, Ehud Friedgut
Chvátal conjectured that every downset has a maximum-size intersecting family which is a star, that is, consists of all members of the downset containing a fixed element. Recently,…
An analogue of Bonami's Lemma for functions on spaces of linear maps, and 2-2 Games
David Ellis, Guy Kindler, Noam Lifshitz
We prove an analogue of Bonami's (hypercontractive) lemma for complex-valued functions on , where and are vector spaces over a finite field. This inequali…
Forbidden intersection problems for families of linear maps
David Ellis, Guy Kindler, Noam Lifshitz
We study an analogue of the Erdős-Sós forbidden intersection problem, for families of linear maps. If and are vector spaces over the same field, we say a family $\mathcal{F…
Small Sets in Union-Closed Families
David Ellis, Maria-Romina Ivan, Imre Leader
Our aim in this note is to show that, for any , there exists a union-closed family with (unique) smallest set such that no element of belongs to more than…
Intersection Problems in Extremal Combinatorics: Theorems, Techniques and Questions Old and New
David Ellis
The study of intersection problems in Extremal Combinatorics dates back perhaps to 1938, when Paul Erdős, Chao Ko and Richard Rado proved the (first) `Erdős-Ko-Rado theorem' on the…
Union-closed families with small average overlap densities
David Ellis
In this very short paper, we point out that the average overlap density of a union-closed family of subsets of may be as small as $Θ((\log \log |\m…