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On the density of sets of divisors

✍ Scribed by R.E.L. Aldred; R.P. Anstee

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
214 KB
Volume
137
Category
Article
ISSN
0012-365X

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✦ Synopsis

Consider the lattice of divisors of n, [1, n]. For any downset (ideal) J 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 J ]. If we let 5 Β’ be the set of minimal elements of [ 1, n] not in J, then we forbid in D the configurations C(s) (defined in the paper) for sE5 e. This generalizes a result of Alon and in turn generalizes a result of Sauer, Perles and Shelah.

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