A Class of Lattices

Jungnickel, Dieter and Leclerc, Matthias (1988) A Class of Lattices.
Published in: Ars Combinatoria Vol. 26. pp. 243-248.


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.

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Item Type: Article
Citations: 3 (Google Scholar) | 2 (Web of Science)
Uncontrolled Keywords: k-uniform matroids lattices trivial Steiner system
  • 05-XX Combinatorics > 05Bxx Designs and configurations > 05B35 Matroids, geometric lattices

  • Divisions: Mathematical Institute
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      Deposit Information:
      ZAIK Number: zpr88-054
      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