Quasi-symmetric designs with fixed difference of block intersection numbers
✍ Scribed by Rajendra M. Pawale
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 112 KB
- Volume
- 15
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
The following results for proper quasi‐symmetric designs with non‐zero intersection numbers x,y and λ > 1 are proved.
Let D be a quasi‐symmetric design with z = y − x and v ≥ 2__k__. If x ≥ 1 + z + z^3^ then λ < x + 1 + z + z^3^.
Let D be a quasi‐symmetric design with intersection numbers x, y and y − x = 1. Then D is a design with parameters v = (1 + m) (2 + m)/2, b = (2 + m) (3 + m)/2, r = m + 3, k = m + 1, λ = 2, x = 1, y = 2 and m = 2,3,… or complement of one of these design or D is a design with parameters v = 5, b = 10, r = 6, k = 3, λ = 3, and x = 1, y = 2.
Let D be a triangle free quasi‐symmetric design with z = y − x and v ≥ 2__k__, then x ≤ z + z^2^.
For fixed z ≥ 1 there exist finitely many triangle free quasi‐symmetric designs non‐zero intersection numbers x, y = x + z.
There do not exist triangle free quasi‐symmetric designs with non‐zero intersection numbers x, y = x + 2.
© 2006 Wiley Periodicals, Inc. J Combin Designs 15: 49–60, 2007