On the density of sets of divisors

Discrete Mathematics (Impact Factor: 0.58). 01/1995; 137(s 1–3):345–349. DOI: 10.1016/0012-365X(93)E0114-J
Source: DBLP

ABSTRACT Consider the lattice of divisors of n, [1, n]. For any downset (ideal) ℐ in [1, n] we get a forbidden configuration theorem of the type that if a set of divisors D avoids certain configurations, then |D|⩾|ℐ|. If we let ℓ be the set of minimal elements of [1, n] not in ℐ, then we forbid in D the configurations C(s) (defined in the paper) for s∈ℒ. This generalizes a result of Alon and in turn generalizes a result of Sauer, Perles and Shelah.

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