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.
By Dimitry Gurevich
By Vincent Rivasseau , Léonard Ferdinand
By James Propp
By Paul-André Melliès
By Alexandros Singh
By Sergey Yurkevich
By Cyril Banderier
By Stéphane Gaubert
By Vincel Hoang Ngoc Minh
By Lionel Pournin
By Claudio Dappiaggi
By Alexander Strohmaier
By Hans Lindblad
By Misha Gromov
By Olivier Benoist
By Viviane Pons
By Viviane Pons
