direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Logo der TU Berlin

Inhalt des Dokuments

Preprint 590-1998

Combinatorial Optimization & Graph Algorithms group (COGA-Preprints)

Interval Reductions and Extensions of Orders: Bijections to Chains in Lattices
Stefan Felsner, Jens Gustedt, and Michel Morvan
extended abstract to appear FPSAC'98
not available
not available
We discuss bijections that relate families of chains in lattices associated to an order P and families of interval orders defined on the ground set of P. Two bijections of this type have been known:par (1) The bijection between maximal chains in the antichain lattice AA(P) and the linear extensions of P. (2) A bijection between maximal chains in the lattice of maximal antichains AAM(P) and minimal interval extensions of P. par We discuss two approaches to associate interval orders to chains in AA(P). This leads to new bijections generalizing Bijections~1 and~2. As a consequence we characterize the chains corresponding to weak-order extensions and minimal weak-order extensions of P. par Seeking for a way of representing interval reductions of P by chains we came up with the separation lattice S(P). Chains in this lattice encode an interesting subclass of interval reductions of P. Let SM(P) be the lattice of maximal separations in the separation lattice. Restricted to maximal separations the above bijection specializes to a bijection which nicely complements 1 and 2.par (3) A bijection between maximal chains in the lattice of maximal separations SM(P) and minimal interval reductions of P.
Download as [ps.gz]
Title: Source

Zusatzinformationen / Extras


Schnellnavigation zur Seite über Nummerneingabe