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Combinatorica

, Volume 35, Issue 2, pp 153–180 | Cite as

Matroid intersection, base packing and base covering for infinite matroids

  • Nathan Bowler
  • Johannes Carmesin
Original Paper

Abstract

As part of the recent developments in infinite matroid theory, there have been a number of conjectures about how standard theorems of finite matroid theory might extend to the infinite setting. These include base packing, base covering, and matroid intersection and union. We show that several of these conjectures are equivalent, so that each gives a perspective on the same central problem of infinite matroid theory. For finite matroids, these equivalences give new and simpler proofs for the finite theorems corresponding to these conjectures.

This new point of view also allows us to extend, and simplify the proofs of some cases where these conjectures were known to be true.

Mathematics Subject Classification (2010)

05C63 05B35 05B40 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversität HamburgHamburgGermany

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