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Dimension of Restricted Classes of Interval Orders

Abstract

Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most \(3\). This article shows that the same dimension bound applies to two other classes of posets: those having a representation consisting of unit intervals (but with a mixture of open and closed intervals allowed) and those having a representation consisting of closed intervals with lengths in \(\left\{ 0,1 \right\}\).

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Acknowledgements

The authors would like to thank an anonymous referee for valuable suggestions that improved the paper.

Funding

This work was supported by a grant from the Simons Foundation (#426725, Ann Trenk).

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Correspondence to Mitchel T. Keller.

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Keller, M.T., Trenk, A.N. & Young, S.J. Dimension of Restricted Classes of Interval Orders. Graphs and Combinatorics 38, 137 (2022). https://doi.org/10.1007/s00373-022-02543-6

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  • DOI: https://doi.org/10.1007/s00373-022-02543-6

Keywords

  • Interval order
  • Dimension
  • Semiorder
  • Unit OC interval order

Mathematics Subject Classification

  • 06A07