Tropical Combinatorics
Tropical Combinatorics
Tropical Combinatorics
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<strong>Tropical</strong> Polynomials<br />
read ordinary (Laurent) polynomial with real coefficients as<br />
function<br />
replace operations “+” and “·” by “⊕” and “⊙”<br />
Example<br />
F(x) := (7 ⊙ x ⊙3 ) ⊕ (3 ⊙ x) ⊕ 4 = min(7 + 3x,3 + x,4)<br />
Definition<br />
tropical polynomial F vanishes at p :⇔ there are at least two<br />
terms where the minimum F(p) is attained<br />
F(1) = min(7 + 3 · 1, 3+1 , 4 ) = 4