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math.CO2024
The external activity complex of a pair of matroids
Andrew Berget, Alex Fink
We introduce the Schubert variety of a pair of linear subspaces in and the external activity complex of a pair of not necessarily realizable matroids. Both of these…
math.CO2024
The omega invariant of a matroid
Alex Fink, Kris Shaw, David E Speyer
The third author introduced the -polynomial of a matroid, a covaluative matroid statistic which is unchanged under series and parallel extension. The -polynomial of…
math.AG2024
Projective hypersurfaces in tropical scheme theory I: the Macaulay ideal
Alex Fink, Jeffrey Giansiracusa, Noah Giansiracusa +1
A "tropical ideal" is an ideal in the idempotent semiring of tropical polynomials that is also, degree by degree, a tropical linear space. We introduce a construction based on tran…