Hochstättler, Winfried and Kern, Walter (1989) Matroid Matching in Pseudomodular Lattices.
Published in: Combinatorica : an international journal on combinatorics and the theory of computing Vol. 9 (2). pp. 145-152.

Abstract

The matroid matching problem (also known as matroid parity problem) has been intensively studied by several authors. Starting from very special problems, in particular the matcing problem and the matroid intersection problem, good characterizations have been obtained for more and more general classes of matroids. The two most recent ones are the class of represetable matroids and, later on, the class of algebraic matroids, cf. L. Lovász [Selecting independent lines from a family of lines in projective space, Acta Sci. Math. 42, 121-131 (1980)] when M is a projective space. Later on, the minimax form and A.W.M. Dress and L. Lovász [On some combinatorial properties of algebraic matroids, Combinatorica 7, 39-48 (1987)]. We present a further step of generalization showing that a good characterization can also be obtained for the class of so-called pseudomodular matroids, introduced by A. Björner and L. Lovász [Acta Sci. Math. 51, No. 3/4, 295-308 (1987)]. A small counterexample is included to show that pseudomodularity still does not cover all matroids that behave well with respect to matroid matching.

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