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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