Subdiagrams equal in number to their duals
Copyright policy )Subdiagrams equal in number to their duals
A subdiagram S of an ordered set P is a cover-preserving ordered subset of P. If S is finite, \(\ell (S)\neq 2\) and S is, as a down set, embedded in a selfdual lattice of subspaces of a projective geometry then the authors prove that S is a ''dual subdiagram invariant'' which means: For any modular lattice M, the number of subdiagrams of M isomorphic to S equals the number of subdiagrams of M dually isomorphic to S.
- University of Ottawa Canada
- Darmstadt University of Applied Sciences Germany
Lattices of subspaces and geometric closure systems, Modular lattices, Desarguesian lattices, modular lattice, dually isomorphic, subdiagrams, Combinatorial structures in finite projective spaces, lattice of subspaces of a projective geometry, Semimodular lattices, geometric lattices
Lattices of subspaces and geometric closure systems, Modular lattices, Desarguesian lattices, modular lattice, dually isomorphic, subdiagrams, Combinatorial structures in finite projective spaces, lattice of subspaces of a projective geometry, Semimodular lattices, geometric lattices
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