2 citations · 2 across the 3 of their papers we have counts for
9 papers
Algebraic and combinatorial expansion in random simplicial complexes
Nikolaos Fountoulakis, Michał Przykucki
In this paper we consider the expansion properties and the spectrum of the combinatorial Laplace operator of a -dimensional Linial-Meshulam random simplicial complex, above the…
High-dimensional bootstrap processes in evolving simplicial complexes
Nikolaos Fountoulakis, Michał Przykucki
We study bootstrap percolation processes on random simplicial complexes of some fixed dimension . Starting from a single simplex of dimension , we build our complex dy…
Shotgun reconstruction in the hypercube
Michał Przykucki, Alexander Roberts, Alex Scott
Mossel and Ross raised the question of when a random colouring of a graph can be reconstructed from local information, namely the colourings (with multiplicity) of balls of given r…
Parking on the integers
Michał Przykucki, Alexander Roberts, Alex Scott
Models of parking in which cars are placed randomly and then move according to a deterministic rule have been studied since the work of Konheim and Weiss in the 1960s. Recently, Da…
Vertex-isoperimetric stability in the hypercube
Michał Przykucki, Alexander Roberts
Harper's Theorem states that, in a hypercube, among all sets of a given fixed size the Hamming balls have minimal closed neighbourhoods. In this paper we prove a stability-like res…
On the critical densities of minor-closed classes
Colin McDiarmid, Michał Przykucki
Given a minor-closed class of graphs, let denote the supremum over all graphs in of the ratio of edges to vertices. We investigate the…