Vol. 81, No. 2, 1979

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Dedekind’s problem: monotone Boolean functions on the lattice of divisors of an integer

Paul Hess

Vol. 81 (1979), No. 2, 411–415
Abstract

This paper is concerned with the combinatorial problem of counting the number of distinct collections of divisors of an integer N having the property that no divisor in a collection is a multiple of any other. It is shown that if N factors into primes N = p1a1p2a2pnan the number of distinct collections of divisors with the stated property does not exceed ( i=1nai n + 3)M, where M is the maximum coefficient in the expansion of the polynomial

(1+ x + x2 + ⋅⋅⋅+xa1)(1+ x +x2 + ⋅⋅⋅+ xa2)⋅⋅⋅(1 + x+ x2 + ⋅⋅⋅+ xan).

Mathematical Subject Classification 2000
Primary: 06B99
Secondary: 05A15
Milestones
Received: 6 April 1978
Revised: 14 September 1978
Published: 1 April 1979
Authors
Paul Hess