2023/09/12 by Adams, Henry, Virk, Žiga · 1 citation
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2309.06222
We provide novel lower bounds on the Betti numbers of Vietoris-Rips complexes of hypercube graphs of all dimensions, and at all scales. In more detail, let Qn be the vertex set of 2n vertices in the n-dimensional hypercube graph, equipped with the shortest path metric. Let VR(Qn;r) be its Vietoris--Rips complex at scale parameter r ≥ 0, which has Qn as its vertex set, and all subsets of diameter at most r as its simplices. For integers r