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Bases in Infinite Matroids
Author(s) -
Aharoni Ron,
Pouzet Maurice
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-44.3.385
Subject(s) - matroid , mathematics , conjecture , extension (predicate logic) , rank (graph theory) , combinatorics , graph , diagonal , discrete mathematics , computer science , geometry , programming language
We consider bases in matroids of infinite rank, and prove: (a) the existence of a perfect matching in the ‘transition graph’ of any two bases. This is an extension of the existence of a non‐zero generalized diagonal in the transition matrix between bases in finite dimensional linear spaces, and settles a conjecture of the second author [8]. (b) A Cantor‐Bernstein theorem for matroids. (c) The existence of a winning strategy for the ‘good guy’ in an exchange game between bases in infinite matroids.