Strongly divisible 1-designs

✍ Scribed by Henry Beker

• Book ID: 104643956
• Publisher: Springer
• Year: 1979
• Tongue: English
• Weight: 691 KB
• Volume: 8
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00151514

✦ Synopsis

If a 1-design, .@, admits a tactical decomposition such that the number of blocks through two distinct points depends only on their point classes and further that the number of blocks through any two distinct points of the same point class is a constant, then the decomposition is called a tactical division. In the case of -~ being a 2-design the terms tactical division and tactical decomposition are synonymous. If the division has c block classes and dpoint classes then b + d ~> v + c where b is the number of blocks of 2 and v is the number of points of-~. Tactical divisions for which b + d = v + c are of special interest and are called strong. A 1-design admitting a strong tactical division is called strongly divisible.

All symmetric and affine 2-designs are strongly divisible and I shall indicate some of the properties of strongly divisible designs that are similar to those of symmetric and affine designs.