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 .
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