English

Dimension of Restricted Classes of Interval Orders

Combinatorics 2022-01-05 v4

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 {0,1}\{0,1\}.

Keywords

Cite

@article{arxiv.2004.08294,
  title  = {Dimension of Restricted Classes of Interval Orders},
  author = {Mitchel T. Keller and Ann N. Trenk and Stephen J. Young},
  journal= {arXiv preprint arXiv:2004.08294},
  year   = {2022}
}

Comments

9 pages, 3 figures