A Class of Lattices
Jungnickel, Dieter and Leclerc, Matthias
(1988)
A Class of Lattices.
Published in:
Ars Combinatoria Vol. 26.
pp. 243-248.
Abstract
We determine the lattice in Z n generated by those vectors having exactly k components 1 and the remaining n-k components 0; we also exhibit a ''nice'' basis for this lattice. Note that the generating vectors are in a natural way associated with well-known combinatorial objects. They are the characteristic vectors of both the blocks of the trivial Steiner system S(k,k,n) and the bases of the k-uniform matroid on n points. We also obtain the corresponding polyhedron and point out an interesting sublattice (in the case n=m² arising from Combinatorial Matrix Theory.
Item Type: | Article |
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Citations: | 3 (Google Scholar) | 2 (Web of Science) |
Uncontrolled Keywords: | k-uniform matroids lattices trivial Steiner system |
Subjects: |
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Divisions: | Mathematical Institute |
Related URLs: |
ZAIK Number: | zpr88-054 |
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Depositing User: | Archive Admin |
Date Deposited: | 02 Apr 2001 00:00 |
Last Modified: | 09 Jan 2012 11:39 |
URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/54 |