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math.CO2026
The parity module of a matroid
Tom Braden, June Huh, Jacob P. Matherne +2
We introduce the parity module of a matroid with coefficients in a field . When has characteristic zero, we show that the parity module of a matroid is iso…
math.CO2026
Chromatic symmetric functions of claw-free graphs are not Schur positive
Jacob P. Matherne, Alejandro H. Morales
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize chromatic polynomials of graphs. In 1995, Stanley introduced these sym…
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…