On an algorithm that generates an interesting maximal set P(n) of the naturals for any n greater than or equal to 2
| dc.creator | Das, Bidu Prakash | |
| dc.creator | Chakraborty, Soubhik | |
| dc.date | 2008-09-17 | |
| dc.date.accessioned | 2026-07-07T10:03:29Z | |
| dc.date.available | 2026-07-07T10:03:29Z | |
| dc.description | The 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.description | There 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.identifier | https://arxiv.org/abs/0809.2884 | |
| dc.identifier | http://arxiv.org/abs/0809.2884 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169308 | |
| dc.subject | Discrete Mathematics | |
| dc.title | On an algorithm that generates an interesting maximal set P(n) of the naturals for any n greater than or equal to 2 | |
| dc.type | text |