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K-polynomials of multiplicity-free varieties

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arxiv 2212.13091 v3 pith:CTDRKKJK submitted 2022-12-26 math.AG math.ACmath.CO

Federico Castillo , Yairon Cid-Ruiz , Fatemeh Mohammadi , Jonathan Montaño This is my paper · ORCID
classification math.AGmath.ACmath.CO
keywords multiplicity-freepolymatroidvarietiesgeneralizedpolynomialpolynomialssupporttwisted
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abstract

We describe the twisted $K$-polynomial of multiplicity-free varieties in a multiprojective setting. More precisely, for multiplicity-free varieties, we show that the support of the twisted $K$-polynomial is a generalized polymatroid. As applications, we show that the support of the M\"obius function of a linear polymatroid is a generalized polymatroid, and we settle a conjecture of Monical, Tokcan and Yong regarding Grothendieck polynomials for the case of zero-one Schubert polynomials.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Syzygies of polymatroidal ideals

    math.AC 2025-07 conditional novelty 7.0 of 10

    For every polymatroid, the cave polynomial is valuative, its support is a generalized polymatroid, and its coefficients are the Möbius values, settling the Bandari-Bayati-Herzog and Castillo-Cid-Ruiz-Mohammadi-Montano...

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    math.CO 2025-05 conditional novelty 7.0 of 10

    Hybrid Grothendieck polynomials unify stable and dual stable Grothendieck polynomials, with proofs of symmetry, Schur expansion, saturated Newton polytopes, and an omega image formula.

  3. Changing Bases with Pipe Dream Combinatorics

    math.CO 2025-06 conditional novelty 6.0 of 10

    New combinatorial formulas, via bumpless pipe dreams and pipe dreams, express Grothendieck polynomials in the Schubert basis and Schubert polynomials in the Grothendieck basis, and extend to the back stable setting.

  4. Three Combinatorial Algorithms for the Cave Polynomial of a Polymatroid

    math.CO 2026-01 accept novelty 5.0 of 10

    Four polynomials of a polymatroid—cave, stalactite, box, and Möbius—are shown to coincide by purely combinatorial coefficient comparisons.

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