Partitionable sets, almost partitionable sets, and their applications

被引：3

作者：

Chang, Yanxun ^{[1
]}

Costa, Simone ^{[2
]}

Feng, Tao ^{[1
]}

Wang, Xiaomiao ^{[3
]}

机构：

[1] Beijing Jiaotong Univ, Dept Math, Beijing, Peoples R China

[2] Univ Brescia, Dipartimento DICATAM, Brescia, Italy

[3] Ningbo Univ, Sch Math & Stat, Ningbo, Zhejiang, Peoples R China

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2020年 / 28卷 / 11期

基金：

中国国家自然科学基金;

关键词：

almost partitionable set; balanced sampling plans excluding contiguous unit; partitionable set; optical orthogonal code; whist tournament; OPTICAL ORTHOGONAL CODES; TRIPLEWHIST TOURNAMENTS; DIFFERENCE-FAMILIES; WHIST TOURNAMENTS; EXISTENCE; CONSTRUCTIONS; DESIGNS; FRAME;

D O I：

10.1002/jcd.21744

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper introduces almost partitionable sets (APSs) to generalize the known concept of partitionable sets. These notions provide a unified frame to construct Z-cyclic patterned starter whist tournaments and cyclic balanced sampling plans excluding contiguous units. The existences of partitionable sets and APSs are investigated. As an application, a large number of optical orthogonal codes achieving the Johnson bound or the Johnson bound minus one are constructed.

引用

页码：783 / 813

页数：31

共 43 条

[1] Existence of directed triplewhist tournaments with the three person property 3P DT Wh(v) [J].

Abel, R. J. R. ;

Bennett, F. E. ;

Ge, Gennian .

DISCRETE APPLIED MATHEMATICS, 2008, 156 (14) :2655-2665

[2] New Z-cyclic triplewhist frames and triplewhist tournament designs [J].

Abel, R. Julian R. ;

Finizio, Norman J. ;

Ge, Gennian ;

Greig, Malcolm .

DISCRETE APPLIED MATHEMATICS, 2006, 154 (12) :1649-1673

[3] Necessary conditions for the existence of two classes of ZCPS-Wh(v) [J].

Abel, R. Julian R. ;

Anderson, Ian ;

Finizio, Norman J. .

DISCRETE APPLIED MATHEMATICS, 2011, 159 (08) :848-851

[4] New product theorems for Z-cyclic whist tournaments [J].

Anderson, I ;

Finizio, NJ ;

Leonard, PA .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 1999, 88 (01) :162-166

[5]

Anderson I., 1995, J COMBIN MATH COMBIN, V19, P129

[6]

ANDERSON I., 1997, COMBINATORIAL DESIGN

[7]

Baker R.D., 1975, Congressus Numerantium, V14, P89

[8]

Baker R. D., WHIST TOURNAME UNPUB

[9]

Bennett FE., 1992, Contemporary Design Theory: A Collection of Surveys, P41

[10] BRIDGE TOURNAMENT PROBLEM AND CALIBRATION DESIGNS FOR COMPARING PAIRS OF OBJECTS [J].

BOSE, RC ;

CAMERON, JM .

JOURNAL OF RESEARCH OF THE NATIONAL BUREAU OF STANDARDS SECTION B-MATHEMATICAL SCIENCES, 1965, B 69 (04) :323-+

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