On equitable zero sums
| dc.creator | Croot, Ernie | |
| dc.creator | Elsholtz, Christian | |
| dc.date | 2007-09-07 | |
| dc.date.accessioned | 2026-07-07T08:28:22Z | |
| dc.date.available | 2026-07-07T08:28:22Z | |
| dc.description | It is well-known that any sequence of at least N integers contains a subsequence whose sum is 0 (mod N). However, there can be very few subsequences with this property (e.g. if the initial sequence is just N 1's, then there is only one subsequence). When the length L of the sequence is much longer, we might expect that there are 2^L/N subsequences with this property (imagine the subsequences have sum-of-terms uniformly distributed modulo N -- the 0 class gets about 2^L/N subsequences); however, it is easy to see that this is actually false. Nonetheless, we are able to prove that if the initial sequence has length at least 4N, and N is odd, then there is a subsequence of length L > N, having at least 2^L/N subsequences that sum to 0 mod N. | |
| dc.description | This is a preliminary draft. Future drafts will have more references, and possibly a stronger main theorem | |
| dc.identifier | https://arxiv.org/abs/0709.1176 | |
| dc.identifier | http://arxiv.org/abs/0709.1176 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137595 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05D99 | |
| dc.title | On equitable zero sums | |
| dc.type | text |