Eric R Ramos

collaborators

3 papers

math.GR2025

Homology of matching complexes and representations of symmetric groups

Michael Bate, Brent Everitt, Sam Ford +1

We compute the homology of the matching complex $M (I^)$ , where $I^$ is the complete hypergraph on $n \geq 2$ vertices, and analyse the $S_{n}$ -representations carried by this homology…

math.CO2025

An AI enhanced approach to the tree unimodality conjecture

Eric Ramos, Sunny Sun

Given a graph $G$ , its independence sequence is the integral sequence $a_{1}, a_{2}, ..., a_{n}$ , where $a_{i}$ is the number of independent sets of vertices of size i. In the late 80's Alavi…

math.CO2024

Independence numbers in certain families of highly symmetric graphs

David Guan, Eric Ramos

FI-graphs were introduced by the second author and White to capture the idea of a family of nested graphs, each member of which is acted on by a progressively larger symmetric grou…