Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 842.11035
Autor: Erdös, Paul; Nicolas, J.L.
Title: On practical partitions. (In English)
Source: Collect. Math. 46, No.1-2, 57-76 (1995).
Review: Let A = {a1 = 1 < a2 < ... < ak < ...} be an infinite subset of N. A partition of n with parts in A is a way of writing n = ai1+ai2+...+aij with 1 \leq i1 \leq i2 \leq ... \leq ij. An integer a is said to be represented by the above partition, if it can be written a = sumjr = 1 \epsilonr air with \epsilonr = 0 or 1. A partition will be called practical if all a's, 1 \leq a \leq n, can be represented. When A = N, it has been proved by P. Erdös and M. Szalay that almost all paritions are practical. In this paper, a similar result is proved, first when ak = 2k, secondly when ak \geq kak-1. Finally an example due to D. Hickerson gives a set A and integers n for which a lot of non practical partitions do exist.
Reviewer: J.L.Nicolas (Villeurbanne)
Classif.: * 11P81 Elementary theory of partitions
11B83 Special sequences of integers and polynomials
Keywords: practical partitions; partition
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