CAT-generation of ideals

Details CAT-generation of ideals CAT-generation of ideals

2010-11-15

arxiv.org/abs/1011.3373v3

Mathematics

Combinatorics

This paper has been withdrawn by the author due to a crucial error

Scientific paper

We consider the problem of generating all ideals of a poset. It is a long standing open problem, whether or not the ideals of any poset can be generated in constant amortized time, CAT for short. We refine the tree traversal, a method introduced by Pruesse and Ruskey in 1993, to obtain a CAT-generator for two large classes of posets: posets of interval dimension at most two and so called locally planar posets. This includes all posets for which a CAT-generator was known before. Posets of interval dimension at most two generalize both, interval orders and 2-dimensional posets. Locally planar posets generalize for example posets with a planar cover graph. We apply our results to CAT-generate all c-orientations of a planar graph. As a special case this is a CAT-generator for many combinatorial objects like domino and lozenge tilings, planar spanning trees, planar bipartite perfect matchings, Schnyder woods, and others.

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