✦ LIBER ✦

Interval orders based on arbitrary ordered sets

✍ Scribed by Jutta Mitas

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 923 KB
Volume: 144
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00288-t

No coin nor oath required. For personal study only.

✦ Synopsis

In general, an interval order is defined to be an ordered set which has an interval representation on a linearly ordered set, the real numbers for example. Bogart et al. (1991) generalized this concept and allowed the underlying set to be weakly ordered. They found a necessary and sufficient condition for an ordered set to be an interval order based on a weak order as well as a characterization for this class of ordered sets by 4 forbidden suborders. In this paper interval orders based on further classes of ordered sets are investigated. Hereby, we concentrate on classes characterized by one forbidden suborder, such as series-parallel orders and interval orders. Furthermore, we analyse connections between order dimension and interval dimension.

📜 SIMILAR VOLUMES

Theorems on intervals of ordered sets

✍ Richard Rado 📂 Article 📅 1981 🏛 Elsevier Science 🌐 English ⚖ 193 KB

VE I) be a family of such intervals. For NE I let V(N) be the chromatic number of the intersection graph 0; (A,,: Y E N), Theorem 1. Zf I is finite and A,, f1.4,,#0 for CL, YE I, tlren n,,, A# 6 Theorem 2. Let k IX a positiw integer and x(N) G k for INI = k + 1. Then x(Z) c k. XlleOrean 3. There is

Confidence intervals based on interpolat

Confidence intervals based on interpolated order statistics

✍ Thomas P Hettmansperger; Simon J Sheather 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 347 KB

Matroids on Partially Ordered Sets

✍ Marilena Barnabei; Giorgio Nicoletti; Luigi Pezzoli 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 346 KB

## L dimension may be chosen within each of the subspaces L in the set S that are ''in general position.'' For example, in the real projective space of dimension 3, consider a plane , a line r not belonging to , the point P [ r l , and two distinct points Q, R both different from P, lying on the l

On c-homogeneous ordered sets

✍ Gerhard Behrendt 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 272 KB

On the Bessel Transformation of Arbitrar

On the Bessel Transformation of Arbitrary Order

✍ J. M. Méndez 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 324 KB

Colorings of diagrams of interval orders

Colorings of diagrams of interval orders and α-sequences of sets

✍ Stefan Felsner; William T. Trotter 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 383 KB

We show that a proper coloring of the diagram of an interval order I may require 1 + I-log 2 height(l)] colors and that 2 + l-log 2 height(I)'] colors always suffice. For the proof of the upper bound we use the following fact: A sequence C 1 ... ## .. C h of sets (of colors) with the property (ct) C