Tropical Combinatorics
Tropical Combinatorics
Tropical Combinatorics
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A <strong>Tropical</strong> Hypersurface<br />
point vi ∈ T d−1 = apex of unique max-tropical hyperplane<br />
H max (vi)<br />
homogeneous linear form hi ∈ C{{z}}[x1, xx, . . .,xd];<br />
h := h1 · h2 · · ·hn<br />
Proposition<br />
The tropical hypersurface defined by trop max (h) is the union of<br />
the max-tropical hyperplanes in A.<br />
Corollary<br />
Let p ∈ T d−1 \ A be a generic point. Then its coarse type tA(p)<br />
equals the exponent of the monomial in h which defines the unique<br />
facet of P(trop max (h)) above p.