7 papers · 1 filter
Random complexes with free involution
Florian Frick, Andrew Newman
We introduce a new model for random simplicial complexes which with high probability generates a complex that has a simply-connected double cover. Hence we develop a model for rand…
Complexes of nearly maximum diameter
Tom Bohman, Andrew Newman
The diameter of a strongly connected -dimensional simplicial complex is the diameter of its dual graph. We provide a probabilistic proof of the existence of -dimensional simp…
Random growth on a Ramanujan graph
Janko Boehm, Michael Joswig, Lars Kastner +1
The behavior of a certain random growth process is analyzed on arbitrary regular and non-regular graphs. Our argument is based on the Expander Mixing Lemma, which entails that the…
Randomized construction of complexes with large diameter
Francisco Criado, Andrew Newman
We consider the question of the largest possible combinatorial diameter among -dimensional simplicial complexes on vertices, denoted . Using a probabilistic c…
The worst way to collapse a simplex
Davide Lofano, Andrew Newman
In general a contractible complex need not be collapsible. Moreover, there exist complexes which are collapsible but even so admit a collapsing sequence where one "gets stuck", tha…
The integer homology threshold in
Andrew Newman, Elliot Paquette
We prove that in the -dimensional Linial--Meshulam stochastic process the st homology group with integer coefficients vanishes exactly when the final isolated …