On Maximum-Sized Near-Regular and -Matroids

 The classes of near-regular and -matroids arise in the study of matroids representable over GF(3) and other fields. For example, a matroid is representable over all fields except possibly GF(2) if and only if it is near-regular, and a matroid is representable over GF(3) and GF(4) if and only if it is a -matroid. This paper determines the maximum sizes of a simple rank-r near-regular and a simple rank-r -matroid and determines all such matroids having these sizes.

Authors and Affiliations

1.  Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA e-mail: oxley@math.lsu.edu, , , , , , US

   James Oxley

2.  Mathematics Department, Louisiana State University, Baton Rouge, LA 70803, USA e-mail: vertigan@math.lsu.edu, , , , , , US

   Dirk Vertigan

3.  Mathematics Department, Victoria University, Wellington, New Zealand e-mail: whittle@kauri.vuw.ac.nz, , , , , , NZ

   Geoff Whittle

Received: July 3, 1996 / Revised: November 21, 1996

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