On an algorithm that generates an interesting maximal set P(n) of the naturals for any n greater than or equal to 2

dc.creatorDas, Bidu Prakash
dc.creatorChakraborty, Soubhik
dc.date2008-09-17
dc.date.accessioned2026-07-07T10:03:29Z
dc.date.available2026-07-07T10:03:29Z
dc.descriptionThe paper considers the problem of finding the largest possible set P(n), a subset of the set N of the natural numbers, with the property that a number is in P(n) if and only if it is a sum of n distinct naturals all in P(n) or none in P(n). Here largest is in the set theoretic sense and n is greater than or equal to 2. We call P(n) a maximal set obeying this property. For small n say 2 or 3, it is possible to develop P(n) intuitively but we strongly felt the necessity of an algorithm for any n greater than or equal to 2. Now P(n) shall invariably be a infinite set so we define another set Q(n) such that Q(n)=N-P(n), prove that Q(n) is finite and, since P(n) is automatically known if Q(n) is known, design an algorithm of worst case O(1) complexity which generates Q(n).
dc.descriptionThere are some problems with the page numbering. I could not remove the unwanted page numbers! please read the pages one after another as they come. There are 11 pages in all
dc.identifierhttps://arxiv.org/abs/0809.2884
dc.identifierhttp://arxiv.org/abs/0809.2884
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169308
dc.subjectDiscrete Mathematics
dc.titleOn an algorithm that generates an interesting maximal set P(n) of the naturals for any n greater than or equal to 2
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