Polymatroid Subdivision
نویسنده
چکیده
A polymatroid rank function on a finite ground set E is a nondecreasing function rk : 2 → R satisfying (0) rk(∅) = 0; (2) rk(A) + rk(B) ≥ rk(A ∩ B) + rk(A ∪ B) for all A,B ⊆ E (the submodular inequality). (Note that everywhere R appears in these notes, any ordered abelian group would do just as well, though if the group is not divisible, some of the integrality statements become unimpressive and we need to be more careful about defining subdivisions.) If moreover rk takes only integer values and (1) rk(A) ≤ |A| for all A ⊆ E then rk is a matroid rank function. Define the independence polytope of rk to be Pind(rk) = {x ∈ R : xi ≥ 0 for all i ∈ E, ∑
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