Scholarlink

<p>We introduce a new type of <i>n</i>-dimensional generalization of symmetric <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((v,k,\lambda )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>v</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> block designs. We prove upper bounds on the dimension&#xa0;<i>n</i> in terms of&#xa0;<i>v</i> and&#xa0;<i>k</i>. We also define the corresponding concept of <i>n</i>-dimensional difference sets, and extend some classic families of difference sets to higher dimensions. Complete classifications are performed for small parameters <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\((v,k,\lambda )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>v</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mi>λ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and some interesting examples are presented.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Projection Cubes of Symmetric Designs

  • 期刊论文

  • 发表日期：

    2025年11月8日

查看全文
  • Vedran Krčadinac,
  • Lucija Relić

摘要

We introduce a new type of n-dimensional generalization of symmetric \((v,k,\lambda )\) ( v , k , λ ) block designs. We prove upper bounds on the dimension n in terms of v and k. We also define the corresponding concept of n-dimensional difference sets, and extend some classic families of difference sets to higher dimensions. Complete classifications are performed for small parameters \((v,k,\lambda )\) ( v , k , λ ) and some interesting examples are presented.