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Matroids on domains of functions.

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Prendergast, Kevin 1980 , 'Matroids on domains of functions.', Unspecified thesis, University of Tasmania.

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Abstract

Any integer-valued function with finite domain E defines, by means of an associated submodular function on 2E , a matroid M(E).
The class pi of matroids so obtained is closed under restriction, contraction, and is self dual. We show it consists precisely of those transversal matroids having a presentation in which the sets of the presentation are nested.
We give an excluded minor characterisation of M .
We count the members of M on an n-set and exhibit explicitly those on a 6-set.
We extend the above investigation, using Rado's Selection Principle, and permitting E to be infinite, to pregeometries.
Finally, by examining some integer-valued functions on Er with r possibly greater than 1, we discuss some of the properties of the class of matroids so obtained.

Item Type: Thesis - Unspecified
Authors/Creators:Prendergast, Kevin
Keywords: Matroids, Functions, Combinatorial analysis
Copyright Holders: The Author
Additional Information:

Thesis (M.Sc.) - University of Tasmania, 1981. Bibliography: l. 75-76

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