Tropical Combinatorics
Tropical Combinatorics
Tropical Combinatorics
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The Coarse Type Ideal<br />
Definition<br />
Let A = A(V ) be an arrangement on n tropical hyperplanes in<br />
T d−1 . The coarse type ideal of A is the monomial ideal<br />
I t(A) = 〈x t(p) : p ∈ T d−1 〉 ⊂ K[x1, . . .,xd]<br />
where x t(p) = x t(p)1<br />
1 x t(p)2<br />
2 · · ·x t(p)d<br />
d .<br />
similar construction for (oriented) matroids<br />
[Novik, Postnikov & Sturmfels 2002]