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COMBINATORICS
2006

On the Symmetry of the Distribution of k-Crossings and k-Nestings in Graphs

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On the Symmetry of the Distribution of k-Crossings and k-Nestings in Graphs
This note contains two results on the distribution of k-crossings and k-nestings in graphs. On the positive side, we exhibit a class of graphs for which there are as many k-noncrossing 2-nonnesting graphs as k-nonnesting 2-noncrossing graphs. This class consists of the graphs on [n] where each vertex x is joined to at most one vertex y with y < x. On the negative side, we show that this is not the case if we consider arbitrary graphs. The counterexample is given in terms of fillings of Ferrers diagrams and solves a problem of Krattenthaler.
Anna de Mier
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where COMBINATORICS
Authors Anna de Mier
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