5 papers · 1 filter
No--in-line problem for
Anubhab Ghosal, Ritesh Goenka, Alexandr Grebennikov +3
What is the maximum number of points one can place in an grid such that every Euclidean line contains at most points? For , this is the notorious no-three-i…
On the largest sum-free subset of the lattice cube
Peter Keevash, Jeck Lim
We determine the limiting density of the largest sum-free subset of the lattice cube for all , thus resolving the natural conjecture that it is constructed…
Balanced two-type annihilation: mean-field asymptotics
John Haslegrave, Peter Keevash
We consider an interacting particle system where equal-sized populations of two types of particles move by random walk steps on a graph, the two types may have different speeds, an…
A very robust Ramsey theorem for matchings
Peter Keevash, Peleg Michaeli
Our main result is a robust generalisation of the Cockayne-Lorimer theorem on the multicolour Ramsey number of matchings. It is moreover a generalisation of the transference genera…
Source localisation in simple random walks
Ritesh Goenka, Peter Keevash, Tomasz PrzybyÅowski
We consider the problem of locating the source (starting vertex) of a simple random walk, given a snapshot of the set of edges (or vertices) visited in the first steps. Conside…