Name
Abstract | ||
|---|---|---|
For each finite field F of prime order there is a constant c such that every 4-connected matroid has at most c inequivalent representations over F. We had hoped that this would extend to all finite fields, however, it was not to be. The (m,n)-mace is the matroid obtained by adding a point freely to M(Km,n). For all n⩾3, the (3,n)-mace is 4-connected and has at least 2n representations over any field F of non-prime order q⩾9. More generally, for n⩾m, the (m,n)-mace is vertically (m+1)-connected and has at least 2n inequivalent representations over any finite field of non-prime order q⩾mm. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jctb.2010.08.001 | Journal of Combinatorial Theory, Series B |
Keywords | Field | DocType |
Matroids,Inequivalent representations,Connectivity | Prime (order theory),Matroid,Combinatorics,Finite field,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
100 | 6 | 0095-8956 |
Citations | PageRank | References |
23 | 1.90 | 0 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| James Oxley | 1 | 397 | 57.57 |
| Dirk Vertigan | 2 | 331 | 32.14 |
| geoff whittle | 3 | 23 | 1.90 |