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Sur les ensembles représentés par les partitions d'un entier n1

✍ Scribed by Marc Deléglise; Paul Erdös; Jean-Louis Nicolas

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
830 KB
Volume
200
Category
Article
ISSN
0012-365X

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✦ Synopsis

Let n=n~ + n2 +... + nj a partition H of n. One will say that this partition represents the integer a if there exists a subsum nq + ni2 + "" + ni~ equal to a. The set g(H) is defined as the set of all integers a represented by/7. Let ~ be a subset of the set of positive integers. We denote by p(~C,n) the number of partitions ofn with parts in ~¢, and by/3(~',n) the number of distinct sets represented by these partitions. Various estimates for b(~C,n) are given. Two cases are more specially studied, when ~' is the set {1,2,4,8, 16 .... } of powers of 2, and when ~¢ is the set of all positive integers. Two partitions of n are said to be equivalent if they represent the same integers. We give some estimations for the minimal number of parts of a partition equivalent to a given partition.

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