Involve: A Journal of Mathematics
- Volume 11, Number 5 (2018), 893-900.
A simple proof characterizing interval orders with interval lengths between 1 and $k$
A poset has an interval representation if each can be assigned a real interval so that in if and only if lies completely to the left of . Such orders are called interval orders. Fishburn (1983, 1985) proved that for any positive integer , an interval order has a representation in which all interval lengths are between and if and only if the order does not contain as an induced poset. In this paper, we give a simple proof of this result using a digraph model.
Involve, Volume 11, Number 5 (2018), 893-900.
Received: 31 August 2017
Revised: 30 January 2018
Accepted: 5 February 2018
First available in Project Euclid: 12 April 2018
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Boyadzhiyska, Simona; Isaak, Garth; Trenk, Ann N. A simple proof characterizing interval orders with interval lengths between 1 and $k$. Involve 11 (2018), no. 5, 893--900. doi:10.2140/involve.2018.11.893. https://projecteuclid.org/euclid.involve/1523498552