3 papers
math.AT2024
Density Sensitive Bifiltered Dowker Complexes via Total Weight
Niklas Hellmer, Jan Spaliński
In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes. Previously, Dowker complexes were studied to address directional o…
math.CO2023
From Erdos-Renyi graphs to Linial-Meshulam complexes via the multineighbor construction
Eric Babson, Jan Spaliński
The -neighbor complex of a graph is the simplicial complex in which faces are sets of vertices with at least common neighbors. We consider these complexes for Erdos-Renyi ra…
math.CO2023
The asymptotic topology of the multineighbor complex of a random graph
Wojciech Matysiak, Jan Spaliński
We introduce the multineighbor complex of a graph, which is a simplicial complex in which a simplex is a subset of the graph with a sufficient number of mutual neighbors. We invest…