K-polynomials of multiplicity-free varieties

Multiplicity-free varieties are those whose multidegrees are equal to zero or one. This special condition implies important arithmetic properties of its coordinate ring and its Gröbner degenerations. In this project, we show that the support of (twisted) K-polynomials of multiplicity-free varieties form a generalized polymatroid. We apply this to show that the Möbius support of a base polymatroid is a generalized polymatroid, and to settle a particular case of a conjecture of Monical, Tokcan, and Yong. This is joint work with Castilllo, Cid-Ruiz, and Mohammadi.