A tropical version of Hilbert function
arxiv(2024)
Abstract
For a tropical prevariety V⊂^n (being a finite union of rational
polyhedra) two tropical polynomials belong to the same congruence class iff
they coincide on V. We define a tropical Hilbert function TH_V(k) as the
dimension of the family of congruence classes of tropical polynomials with
tropical degree at most k. It is shown that TH_V(k) coincides with a
polynomial of degree V for sufficiently big k when V is a
polyhedron. For an arbitrary tropical prevariety we formulate it as a
conjecture. The conjecture is justified in case V =0.
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