Egalitarian Steiner quadruple systems of doubly even order
Egalitarian Steiner quadruple systems of doubly even order
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DOI：
10.1016/j.disc.2022.112887
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发表时间：
2022-07
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影响因子：
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通讯作者：
C. Colbourn
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文献类型：
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作者：
C. Colbourn
对设计的块进行排序，元素的点和是包含该元素的块的索引之和。受欢迎程度的块标记要求点数和尽可能相等。当所有点的总和相等时，系统是平等主义的；当点数总和最多相差1时，它几乎是平等主义的。对于Steiner四重系统，采用一种双重构造来证明当v≡4,20 （mod 24）时存在平均S (3,4, v)，并且当v≡8,16 （mod 24）且v≠8时存在几乎平均S （3,4, v）。
Ordering the blocks of a design, the point sum of an element is the sum of the indices of blocks containing that element. Block labelling for popularity asks for the point sums to be as equal as possible. When all point sums are equal, the system is egalitarian; when point sums differ by at most one, it is almost egalitarian. For Steiner quadruple systems, a doubling construction is adapted to establish that an egalitarian S (3, 4, v) exists whenever v≡ 4, 20 (mod 24) and that an almost egalitarian S (3, 4, v) exists whenever v≡ 8, 16 (mod 24) and v≠ 8.