On Covering Numbers, Young Diagrams, and the Local Dimension of Posets

@article{Damasdi2020OnCN,
  title={On Covering Numbers, Young Diagrams, and the Local Dimension of Posets},
  author={G'abor Dam'asdi and Stefan Felsner and Ant{\'o}nio Gir{\~a}o and Bal{\'a}zs Keszegh and David Lewis and D{\'a}niel T. Nagy and Torsten Ueckerdt},
  journal={ArXiv},
  year={2020},
  volume={abs/2001.06367}
}
We study covering numbers and local covering numbers with respect to difference graphs and complete bipartite graphs. In particular we show that in every cover of a Young diagram with $\binom{2k}{k}$ steps with generalized rectangles there is a row or a column in the diagram that is used by at least $k+1$ rectangles, and prove that this is best-possible. This answers two questions by Kim, Martin, Masa{ř}{\'i}k, Shull, Smith, Uzzell, and Wang (Europ. J. Comb. 2020), namely: - What is the local… 
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