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math.CO2020
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…
math.CO2019
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…
math.CO2018
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…