Weak Maps and Stabilizers of Classes of Matroids

Advances in Applied Mathematics

Volumn 21, Issue 2, 1998, Pages 305-341

  Geelen, James ^a   Oxley, James ^b   Vertigan, Dirk ^b   Whittle, Geoff ^c  

^a UNIVERSITY OF WATERLOO   (Canada)

^b LOUISIANA STATE UNIVERSITY   (United States)

^c VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008383160     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1998.0600     Document Type: Article

References (25)

1. Bixby R. E. On Reid's characterization of the ternary matroids. J. Combin. Theory Ser. B. 26:1979;174-204.
2. Bixby R. E. A simple theorem on 3-connectivity. Linear Algebra Appl. 45:1982;123-126.
3. Cheung A., Crapo H. On relative position in extensions of combinatorial geometries. J. Combin. Theory Ser. B. 44:1988;201-229.
4. Crapo H. Single-element extensions of matroids. J. Res. Nat. Bur. Standards Sect. B. 69:1965;55-65.
5. Ding G., Oporowski B., Oxley J. G., Vertigan D. L. Unavoidable minors of large 3-connected matroids. J. Combin. Theory Ser. B. 71:1997;244-293.
6. Duke R. Freedom in matroids. Ars Combin. 26B:1988;191-216.
7. J. F. Geelen, The excluded-minor characterization of near-regular matroids.
8. J. F. Geelen, A. M. H. Gerards, A. Kapoor, The excluded minors forGF.
9. J. F. Geelen, J. G. Oxley, D. L. Vertigan, G. P. Whittle, Decomposition of [equation].
10. J. F. Geelen, J. G. Oxley, D. L. Vertigan, G. P. Whittle, On totally free expansions of matroids.
11. Kahn J. On the uniqueness of matroid representation overGF. Bull. London Math. Soc. 20:1988;5-10.
12. Lucas D. Weak maps of combinatorial geometries. Trans. Amer. Math. Soc. 206:1975;247-279.
13. Oxley J. G. Matroid Theory. 1992;Oxford Univ. Press, New York.
14. Oxley J. G., Vertigan D. L., Whittle G. P. On inequivalent representations of matroids over finite fields. J. Combin. Theory Ser. B. 67:1996;325-343.
15. Oxley J. G., Whittle G. P. On weak maps of ternary matroids. European J. Combin. 19:1998;377-389.
16. Oxley J. G., Whittle G. P. A note on the non-spanning circuits of a matroid. European J. Combin. 12:1991;259-261.
17. Semple C. A., Whittle G. P. Partial fields and matroid representation. Adv. in Appl. Math. 17:1996;184-208.
18. Seymour P. D. Matroid representation overGF. J. Combin. Theory Ser. B. 26:1979;159-173.
19. Seymour P. D. Decomposition of regular matroids. J. Combin. Theory Ser. B. 28:1980;305-359.
20. Tutte W. T. A homotopy theorem for matroids, I, II. Trans. Amer. Math. Soc. 88:1958;144-174.
21. Tutte W. T. Connectivity in matroids. Canad. J. Math. 18:1966;1301-1324.
22. D. L. Vertigan, Matroid representation over partial fields.
23. Whittle G. P. A characterisation of the matroids representable overGF. J. Combin. Theory Ser. B. 65:1995;222-261.
24. Whittle G. P. On matroids representable overGF. Trans. Amer. Math. Soc. 349:1997;579-603.
25. G. P. Whittle, Stabilizers of classes of representable matroids, J. Combin Theory Ser. B.