A new proof for Zassenhaus-Groemer-Oler inequality

Qinghai Liu; Xiang Li; Lidong Wu; H. A.I. Du; Zhao Zhang; Weili Wu; Xiaodong Hu; Yinfeng Xu

doi:10.1142/S1793830912500140

A new proof for Zassenhaus-Groemer-Oler inequality

Qinghai Liu
, Xiang Li
, Lidong Wu
, H. A.I. Du
, Zhao Zhang
, Weili Wu
, Xiaodong Hu
, Yinfeng Xu

School of Management

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper, we present a new proof for a well-known inequality, conjectured by Zassenhaus in 1947 and proved independently by Groemer in 1960 and Oler in 1961. The inequality gives an upper bound for the number of nonoverlapping unit discs whose centers can be packed into a compact convex region, and recently obtains a lot of applications in study of sensor networks.

Original language	English
Article number	1250014
Journal	Discrete Mathematics, Algorithms and Applications
Volume	4
Issue number	2
DOIs	https://doi.org/10.1142/S1793830912500140
State	Published - 1 Jun 2012

Keywords

Disc packing
Sensor network

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10.1142/S1793830912500140

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title = "A new proof for Zassenhaus-Groemer-Oler inequality",

abstract = "In this paper, we present a new proof for a well-known inequality, conjectured by Zassenhaus in 1947 and proved independently by Groemer in 1960 and Oler in 1961. The inequality gives an upper bound for the number of nonoverlapping unit discs whose centers can be packed into a compact convex region, and recently obtains a lot of applications in study of sensor networks.",

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AU - Du, H. A.I.

AU - Zhang, Zhao

AU - Wu, Weili

AU - Hu, Xiaodong

AU - Xu, Yinfeng

PY - 2012/6/1

Y1 - 2012/6/1

N2 - In this paper, we present a new proof for a well-known inequality, conjectured by Zassenhaus in 1947 and proved independently by Groemer in 1960 and Oler in 1961. The inequality gives an upper bound for the number of nonoverlapping unit discs whose centers can be packed into a compact convex region, and recently obtains a lot of applications in study of sensor networks.

AB - In this paper, we present a new proof for a well-known inequality, conjectured by Zassenhaus in 1947 and proved independently by Groemer in 1960 and Oler in 1961. The inequality gives an upper bound for the number of nonoverlapping unit discs whose centers can be packed into a compact convex region, and recently obtains a lot of applications in study of sensor networks.

KW - Disc packing

KW - Sensor network

UR - https://www.scopus.com/pages/publications/85048226381

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DO - 10.1142/S1793830912500140

M3 - 文章

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A new proof for Zassenhaus-Groemer-Oler inequality

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Keywords

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