论文信息 - Degrees of freedom versus dimension for containment orders

Degrees of freedom versus dimension for containment orders

Given a family of sets L, where the sets in L admit k ‘degrees of freedom’, we prove that not all (k+1)-dimensional posets are containment posets of sets in L. Our results depend on the following enumerative result of independent interest: Let P(n, k) denote the number of partially ordered sets on n labeled elements of dimension k. We show that log P(n, k)∼nk log n where k is fixed and n is large.

Noga Alon | Edward R. Scheinerman | N. Alon | E. Scheinerman

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