On the unique representability of spikes over prime fields
| dc.creator | Wu, Zhaoyang | |
| dc.creator | Sun, Zhi-Wei | |
| dc.date | 2006-06-28 | |
| dc.date | 2006-12-04 | |
| dc.date.accessioned | 2026-07-07T07:17:47Z | |
| dc.date.available | 2026-07-07T07:17:47Z | |
| dc.description | For an integer $n>2$, a rank-$n$ matroid is called an $n$-spike if it consists of $n$ three-point lines through a common point such that, for all $k\in\{1, 2, ..., n - 1\}$, the union of every set of $k$ of these lines has rank $k+1$. Spikes are very special and important in matroid theory. In 2003 Wu found the exact numbers of $n$-spikes over fields with 2, 3, 4, 5, 7 elements, and the asymptotic values for larger finite fields. In this paper, we prove that, for each prime number $p$, a $GF(p$) representable $n$-spike $M$ is only representable on fields with characteristic $p$ provided that $n \ge 2p-1$. Moreover, $M$ is uniquely representable over $GF(p)$. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0606708 | |
| dc.identifier | http://arxiv.org/abs/math/0606708 | |
| dc.identifier | Discrete Math. 306(2006), 1798-1804 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114065 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05B35; 11B75; 11T99 | |
| dc.title | On the unique representability of spikes over prime fields | |
| dc.type | text |