88 citations · 227 across the 22 of their papers we have counts for
4 papers · 2 filters
Special cycles in independence complexes and superfrustration in some lattices
Michal Adamaszek
We prove that the independence complexes of some grids have exponential Betti numbers. This corresponds to the number of ground states in the hard-core model in statistical physics…
Extremal problems related to Betti numbers of flag complexes
Michal Adamaszek
We study the problem of maximizing Betti numbers of simplicial complexes. We prove an upper bound of 1.32^n for the sum of Betti numbers of any n-vertex flag complex and 1.25^n for…
Splittings of independence complexes and the powers of cycles
Michal Adamaszek
We use two cofibre sequences to identify some combinatorial situations when the independence complex of a graph splits into a wedge sum of smaller independence complexes. Our main…
Clique complexes and graph powers
Michal Adamaszek
We study the behaviour of clique complexes of graphs under the operation of taking graph powers. As an example we compute the clique complexes of powers of cycles, or, in other wor…