Maximal Sidon Sets and Matroids
| dc.creator | da Silva, J. A. Dias | |
| dc.creator | Nathanson, Melvyn B. | |
| dc.date | 2005-04-11 | |
| dc.date.accessioned | 2026-07-07T05:19:00Z | |
| dc.date.available | 2026-07-07T05:19:00Z | |
| dc.description | Let X be a subset of an abelian group and a_1,...,a_h,a'_1,...,a'_h a sequence of 2h elements of X such that a_1 + ... + a_h = a'_1 + ... + a'_h. The set X is a Sidon set of order h if, after renumbering, a_i = a'_i for i = 1,..., h. For k \leq h, the set X is a generalized Sidon set of order (h,k), if, after renumbering, a_i = a'_i for i = 1,..., k. It is proved that if X is a generalized Sidon set of order (2h-1,h-1), then the maximal Sidon sets of order h contained in X have the same cardinality. Moreover, X is a matroid where the independent subsets of X are the Sidon sets of order h. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0504226 | |
| dc.identifier | http://arxiv.org/abs/math/0504226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74863 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B34; 11B75; 05B35; 05A17; 05B40 | |
| dc.title | Maximal Sidon Sets and Matroids | |
| dc.type | text |