What question did this study set out to answer?

This work aims to establish formulas for the Hilbert series of Chow rings related to polymatroids and building sets.

August 13, 2026Selecta MathematicaOpen Access

Building sets, Chow rings, and their Hilbert series

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Randomized trial finds new formulas for Hilbert series in building sets, suggesting insights into matroid theory.

This work aims to establish formulas for the Hilbert series of Chow rings related to polymatroids and building sets.
Derived formulas for the Hilbert series of Chow rings using building sets.
Investigated braid matroids and minimal building sets, producing Poincaré polynomials for the moduli space \overline{\mathcal {M}}_{0,n+1}.
Provided examples of matroids with non-log-concave coefficients in their Chow rings.
Formulated new Poincaré polynomials for pointed stable rational curves from minimal building sets.
Demonstrated examples where Chow rings have Hilbert series with non-log-concave coefficients, contrasting with prior conjectures.
Recovered results from Keel, Getzler, Manin, and Aluffi–Marcolli–Nascimento.

Eur et al. (2026) studied this question.

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