5 citations · 6 across the 5 of their papers we have counts for
6 papers
Hypercontractivity for global functions and sharp thresholds
Peter Keevash, Noam Lifshitz, Eoin Long +1
The classical hypercontractive inequality for the noise operator on the discrete cube plays a crucial role in many of the fundamental results in the Analysis of Boolean functions,…
Forbidden vector-valued intersections
Peter Keevash, Eoin Long
We solve a generalised form of a conjecture of Kalai motivated by attempts to improve the bounds for Borsuk's problem. The conjecture can be roughly understood as asking for an ana…
A stability result for the cube edge isoperimetric inequality
Peter Keevash, Eoin Long
We prove the following stability version of the edge isoperimetric inequality for the cube: any subset of the cube with average boundary degree within of the minimum possible i…
Packing and counting arbitrary Hamilton cycles in random digraphs
Asaf Ferber, Eoin Long
We prove packing and counting theorems for arbitrarily oriented Hamilton cycles in for nearly optimal (up to a factor). In particular, we show that g…
Long geodesics in subgraphs of the cube
Imre Leader, Eoin Long
A path in the hypercube is said to be a geodesic if no two of its edges are in the same direction. Let be a subgraph of with average degree . How long a geodesic…
Tilted Sperner Families
Imre Leader, Eoin Long
Let \cal A be a family of subsets of an n-set such that \cal A does not contain distinct sets A and B with |A\B| = 2|B\A|. How large can \cal A be? Our aim in this note is to deter…