We define Hilbert function of a semiring ideal of tropical polynomials in n variables. For n=1 we prove that it is the sum of a linear function and a periodic function (for sufficiently large values). The leading coefficient of the linear function equals the tropical entropy of the ideal. For an arbitrary n we discuss a conjecture that the tropical Hilbert function of a radical ideal is a polynomial of degree at most n−1 (for sufficiently large values). For n=1 the conjecture is true, also we have proved it for zero-dimensional ideals and for planar tropical curves.
De Dimitry Gurevich
De James Propp
De Paul-André Melliès
De Alexandros Singh
De Sergey Yurkevich
De Cyril Banderier
De Stéphane Gaubert
De Vincel Hoang Ngoc Minh
De Lionel Pournin
De Claudio Dappiaggi
De Alexander Strohmaier
De Hans Lindblad
De Olivier Benoist
De Viviane Pons
