Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2223

Preprint Number 2223

Previous Next Preprint server

2223. Antongiulio Fornasiero and Elliot Kaplan
Hilbert polynomials for finitary matroids

Submission date: 2 August 2022


We consider a tuple Φ = (φ_1,...,\phi_m) of commuting maps on a finitary matroid X. We show that if Φ satisfies certain conditions, then for any finite set A ⊆ X, the rank of {φ_1^{r_1}...φ_m^{r_m}(a) : a in A and r_1+...+r_m = t} is eventually a polynomial in t (we also give a multivariate version of the polynomial). This allows us easily recover Khovanskii's theorem on the growth of sumsets, the existence of the classical Hilbert polynomial, and the existence of the Kolchin polynomial. We also prove some new Kolchin polynomial results for differential exponential fields and derivations on o-minimal fields.

Mathematics Subject Classification: Primary 05B35. Secondary 03C64, 05E40, 12H05, 12H10, 13D40

Keywords and phrases:

Full text arXiv 2208.01560: pdf, ps.

Last updated: August 9 2022 14:06 Please send your corrections to: