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math.CO2026
Universality in the algebra and topology of cographs
Adityo Mamun, Jonathan Nalikka, Eric Ramos
A finite simple graph is called a cograph if it does not contain the path on four vertices as an induced subgraph. It is classically known that the family of cographs are…
math.AT2026
Computing stable homology representations of graph configuration spaces
Eric Ramos, Claudia He Yun
Configuration spaces of graphs frequently grow factorially in complexity with the number of particles they parametrize. However, for suitable families of nested graphs …
math.CO2026
Universality theorems for generalized splines
Jacob Matherne, Eric Ramos, Julianna Tymoczko
We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, whi…