Tropical Combinatorics
Tropical Combinatorics
Tropical Combinatorics
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201 111 021<br />
300 210 030<br />
chain complex<br />
with img φ1 = I<br />
003 ideal<br />
012<br />
An Example<br />
I = 〈x 3 1, x 2 1x2, x 3 2, x 2 1x3,<br />
x1x2x3, x 2 2x3, x2x 2 3, x 3 3〉<br />
lcm condition <br />
labels for all cells<br />
f(P) = (8, 11, 4)<br />
check condition for each<br />
b ∈ Z d<br />
e.g., b = (2,2,2)<br />
minimal resolution<br />
F P 4 φ3 11<br />
• : 0 → S −→ S φ2 8<br />
−→ S φ1<br />
−→ S → 0
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