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

@article{Mier2007knoncrossingAK,
title={k-noncrossing and k-nonnesting graphs and fillings of ferrers diagrams},
author={Anna de Mier},
journal={Combinatorica},
year={2007},
volume={27},
pages={699-720}
}
• A. Mier
• Published 9 February 2006
• Mathematics
• Combinatorica
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…

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