# k-noncrossing and k-nonnesting graphs and fillings of ferrers diagrams

@article{Mier2006knoncrossingAK, title={k-noncrossing and k-nonnesting graphs and fillings of ferrers diagrams}, author={Anna de Mier}, journal={Combinatorica}, year={2006}, volume={27}, pages={699-720} }

We give a correspondence between graphs with a given degree sequence and fillings of Ferrers diagrams by nonnegative integers with prescribed row and column sums. In this setting, k-crossings and k-nestings of the graph become occurrences of the identity and the antiidentity matrices in the filling. We use this to show the equality of the numbers of k-noncrossing and k-nonnesting graphs with a given degree sequence. This generalizes the analogous result for matchings and partition graphs of…

## 52 Citations

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