The Postage Stamp Problem and Essential Subsets in Integer Bases
| dc.creator | Hegarty, Peter | |
| dc.date | 2008-07-02 | |
| dc.date.accessioned | 2026-07-07T09:48:11Z | |
| dc.date.available | 2026-07-07T09:48:11Z | |
| dc.description | Plagne recently determined the asymptotic behavior of the function E(h), which counts the maximum possible number of essential elements in an additive basis for N of order h. Here we extend his investigations by studying asymptotic behavior of the function E(h,k), which counts the maximum possible number of essential subsets of size k, in a basis of order h. For a fixed k and with h going to infinity, we show that E(h,k) = Θ_{k} ([h^{k}/\log h]^{1/(k+1)}). The determination of a more precise asymptotic formula is shown to depend on the solution of the well-known "postage stamp problem" in finite cyclic groups. On the other hand, with h fixed and k going to infinity, we show that E(h,k) \sim (h-1) {\log k \over \log \log k}. | |
| dc.description | 15 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0807.0463 | |
| dc.identifier | http://arxiv.org/abs/0807.0463 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164121 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B13, 11B34 | |
| dc.title | The Postage Stamp Problem and Essential Subsets in Integer Bases | |
| dc.type | text |