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.

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