Unlabeled equivalence for matroids representable over finite fields

Details Unlabeled equivalence for matroids representable over finite fields Unlabeled equivalence for matroids representable over finite fields

2012-02-10

arxiv.org/abs/1202.2247v1

Mathematics

Combinatorics

Scientific paper

We present a new type of equivalence for representable matroids that uses the automorphisms of the underlying matroid. Two $r\times n$ matrices $A$ and $A'$ representing the same matroid $M$ over a field $F$ are {\it geometrically equivalent representations} of $M$ if one can be obtained from the other by elementary row operations, column scaling, and column permutations. Using geometric equivalence, we give a method for exhaustively generating non-isomorphic matroids representable over a finite field $GF(q)$, where $q$ is a power of a prime.

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