Jump number and width
type: Item
instance of: scholarly article
title: Jump number and width
zbMATH Open document ID: 0646.06001
DOI: 10.1007/BF00400286
author: Pavol Hell
author: James H. Schmerl
author: Weixuan Li
published in: Order
publication date: 1986-01-01T00:00:00Z
review text: Supposing all ordered sets considered in this paper are finite, the authors define the width w(P), the jump number s(P) and a tower number t(P) of an ordered set P. Then they give the proofs that the maximum jump number of ordered sets having width w and tower number t, denoted by s(w,t), satisfies \(c_ 1tw \lg w\leq s(w,t)\leq c_ 2tw \lg w\) for some positive constants \(c_ 1\) and \(c_ 2\). They also give an answer to problem 15 posed by \textit{W. T. Trotter} [Problems and conjectures in the combinatorial theory of ordered sets, Preprint (1986)], i.e. when w and t are sufficiently large and w is a power of 2, then \((-\epsilon)tw \lg w\leq s(w,t)<(7/10)tw \lg w.\)
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4053689
zbMATH Keywords: jump number
zbMATH Keywords: tower number
MaRDI profile type: Publication
cites work: Ordered sets with small width and large jump number
cites work: Q3815303
full work available at URL: https://doi.org/10.1007/bf00400286
OpenAlex ID: W2093370500
description: scientific article; zbMATH DE number 4053689