Tiling groups with difference sets

被引：0

作者：

Custic, Ante ^{[1
]}

Krcadinac, Vedran ^{[2
]}

Zhou, Yue ^{[3
]}

机构：

[1] Simon Fraser Univ, Dept Math, Surrey, BC V3T 0A3, Canada

[2] Univ Zagreb, Fac Sci, Dept Math, HR-10000 Zagreb, Croatia

[3] Univ Magdeburg, Fac Math, D-39106 Magdeburg, Germany

来源：

ELECTRONIC JOURNAL OF COMBINATORICS | 2015年 / 22卷 / 02期

基金：

中国国家自然科学基金;

关键词：

difference set; tiling; CONSTRUCTIONS; FAMILIES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study tilings of groups with mutually disjoint difference sets. Some necessary existence conditions are proved and shown not to be sufficient. In the case of tilings with two difference sets we show the equivalence to skew Hadamard difference sets, and prove that they must be normalized if the group is abelian. Furthermore, we present some constructions of tilings based on cyclotomy and investigate tilings consisting of Singer difference sets.

引用

页数：13

共 27 条

[1]

[Anonymous], 1971, CYCLIC DIFFERENCE SE

[2]

[Anonymous], 2003, T48 HELS U TECHN

[3]

Beth T., 1999, DESIGN THEORY, DOI 10.1017/CBO9781139507660

[4]

Buratti M, 2010, ELECTRON J COMB, V17

[5]

Camion P., 1972, J NUMBER THEORY, V4, P266

[6] Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in PG(3, 32h+1) [J].

Ding, Cunsheng ;

Wang, Zeying ;

Xiang, Qing .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2007, 114 (05) :867-887

[7] A family of skew Hadamard difference sets [J].

Ding, Cunsheng ;

Yuan, Jin .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2006, 113 (07) :1526-1535

[8] Block disjoint difference families for Steiner triple systems:: v ≡ 3 mod 6 [J].

Dinitz, JH ;

Shalaby, N .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2002, 106 (1-2) :77-86

[9] Cyclotomic constructions of skew Hadamard difference sets [J].

Feng, Tao ;

Xiang, Qing .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2012, 119 (01) :245-256

[10] Non-abelian skew Hadamard difference sets fixed by a prescribed automorphism [J].

Feng, Tao .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (01) :27-36

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