Name
Abstract | ||
|---|---|---|
Suppose that $q$ is a prime power exceeding five. For every integer $N$ there exists a 3-connected GF($q$)-representable matroid that has at least $N$ inequivalent GF($q$)-representations. In contrast to this, Geelen, Oxley, Vertigan and Whittle have conjectured that, for any integer $r 2$, there exists an integer $n(q,\, r)$ such that if $M$ is a 3-connected GF($q$)-representable matroid and $M$ has no rank-$r$ free-swirl or rank-$r$ free-spike minor, then $M$ has at most $n(q,\, r)$ inequivalent GF($q$)-representations. The main result of this paper is a proof of this conjecture for Zaslavsky's class of bias matroids. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1017/S0963548305006838 | Combinatorics, Probability & Computing |
Keywords | Field | DocType |
main result,bias matroids,3-connected gf,prime power,representable matroid,inequivalent gf,inequivalent representations | Integer,Matroid,Discrete mathematics,Combinatorics,Existential quantification,Conjecture,Prime power,Mathematics | Journal |
Volume | Issue | ISSN |
14 | 4 | 0963-5483 |
Citations | PageRank | References |
0 | 0.34 | 10 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dillon Mayhew | 1 | 102 | 18.63 |