This paper considers representations of ternary matroids over fields other than GF(3). It is shown that a 3-connected ternary matroid representable over a finite field F has at most IFI -2 inequivalent representations over F. This resolves a special case of a conjecture of Kahn in the affirmative.
โฆ LIBER โฆ
Inequivalent representations of matroids having no U3,6-minor
โ Scribed by Jim Geelen; Dillon Mayhew; Geoff Whittle
- Book ID
- 108167361
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 251 KB
- Volume
- 92
- Category
- Article
- ISSN
- 0095-8956
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Kahn conjectured in 1988 that, for each prime power q, there is an integer n(q) such that no 3-connected GF(q)-representable matroid has more than n(q) inequivalent GF(q)-representations. At the time, this conjecture was known to be true for q=2 and q=3, and Kahn had just proved it for q=4. In this
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