4 papers
An AI enhanced approach to the tree unimodality conjecture
Eric Ramos, Sunny Sun
Given a graph , its independence sequence is the integral sequence , where is the number of independent sets of vertices of size i. In the late 80's Alavi…
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…
The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology
Luigi Caputi, Carlo Collari, Eric Ramos
Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to…
Homology of matching complexes and representations of symmetric groups
Michael Bate, Brent Everitt, Sam Ford +1
We compute the homology of the matching complex , where is the complete hypergraph on vertices, and analyse the -representations carried by this homology.…