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On the Unique Representability of Spikes Over Prime Fields by Zhaoyang Wu; Zhi-Wei Sun is a Computer Science article available to read on EtoBox.

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For an integer n 3, 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. Wu [On the number of spikes over finite fields, Discrete Math. 265 (2003) 261-296] 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 is only representable on fields with characteristic p provided that n 2p -1. Moreover, M is uniquely representable over GF(p).

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Author

Zhaoyang Wu; Zhi-Wei Sun

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0012-365X)

Published

2006

Language

EN

Field

Computer Science (Physical Sciences)