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2018 A simple proof characterizing interval orders with interval lengths between 1 and $k$
Simona Boyadzhiyska, Garth Isaak, Ann N. Trenk
Involve 11(5): 893-900 (2018). DOI: 10.2140/involve.2018.11.893

Abstract

A poset P=(X,) has an interval representation if each xX can be assigned a real interval Ix so that xy in P if and only if Ix lies completely to the left of Iy. Such orders are called interval orders. Fishburn (1983, 1985) proved that for any positive integer k, an interval order has a representation in which all interval lengths are between 1 and k if and only if the order does not contain (k+2)+1 as an induced poset. In this paper, we give a simple proof of this result using a digraph model.

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Simona Boyadzhiyska. Garth Isaak. Ann N. Trenk. "A simple proof characterizing interval orders with interval lengths between 1 and $k$." Involve 11 (5) 893 - 900, 2018. https://doi.org/10.2140/involve.2018.11.893

Information

Received: 31 August 2017; Revised: 30 January 2018; Accepted: 5 February 2018; Published: 2018
First available in Project Euclid: 12 April 2018

zbMATH: 1385.05057
MathSciNet: MR3784035
Digital Object Identifier: 10.2140/involve.2018.11.893

Subjects:
Primary: 05C62, 06A99

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2018
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