On Lander's conjecture for difference sets whose order is a power of 2 or 3

Ka Hin Leung; Siu Lun Ma; Bernhard Schmidt

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On Lander's conjecture for difference sets whose order is a power of 2 or 3

机译：关于顺序为2或3的幂的差分集的Lander猜想

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摘要

Let p be a prime and let b be a positive integer. If a (v, k,λ,n) difference set D of order n = p~b exists in an abelian group with cyclic Sylow p-subgroup S, then p ∈ {2,3} and |S| = p. Furthermore, either p = 2 and v = λ = 2 (mod 4) or the parameters of D belong to one of four families explicitly determined in our main theorem.

机译：设p为素数，b为正整数。如果在具有循环Sylow p-子群S的阿贝尔群中存在阶数n = p〜b的（v，k，λ，n）差集D，则p∈{2,3}和| S |。 = p。此外，p = 2和v =λ= 2（模4）或D的参数属于在我们的主定理中明确确定的四个族之一。

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来源
《Designs, Codes and Crytography》 |2010年第1期|P.79-84|共6页
作者
Ka Hin Leung; Siu Lun Ma; Bernhard Schmidt;
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作者单位

Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore;

rnDepartment of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260, Republic of Singapore;

rnDivision of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
difference sets; lander's conjecture; field descent;

机译：差异集;着陆器的推测;场下降;

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1. On Lander’s conjecture for difference sets whose order is a power of 2 or 3 [J] . Ka Hin Leung, Siu Lun Ma, Bernhard Schmidt Designs, Codes and Cryptography . 2010,第1期

机译：在兰德关于差集的猜想中，该差集的阶次为2或3
2. Nonexistence of Abelian difference sets: Lander's conjecture for prime power orders [J] . Leung KH, Ma SL, Schmidt B Transactions of the American Mathematical Society . 2004,第11期

机译：Abelian差异集的不存在：主要功率阶的Lander猜想
3. Hadamard difference sets related to Lander's conjecture [J] . Tao Feng, Ka Hin Leung, Bernhard Schmidt, Journal of Algebra . 2014,第Null期

机译：Hadamard与Lander猜想有关的差异集
4. On Set Expansion Problems and the Small Set Expansion Conjecture [C] . Rajiv Gandhi, Guy Kortsarz International workshop on graph-theoretic concepts in computer science . 2014

机译：关于集展开问题和小集展开猜想
5. Divisible difference sets and difference sets from cyclotomy. [D] . Liu, Kan. 1999

机译：可分差异集和切开术的差异集。
6. Genetic differences in fruit-set patterns are determined by differences in fruit sink strength and a source : sink threshold for fruit set [O] . A. M. Wubs, Y. Ma, E. Heuvelink, 2009

机译：坐果模式的遗传差异取决于果实的下沉强度和来源：下垂的下沉阈值
7. Nonexistence of abelian difference sets: Lander’s conjecture for prime power orders [O] . Ka Hin Leung, Siu Lun Ma, Bernhard Schmidt 2003

机译：阿贝尔差异集的不存在：着陆器猜测主要电源订单

On Lander's conjecture for difference sets whose order is a power of 2 or 3

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