On extensions of some block designs
- Authors: Makhnev A.A.1
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Affiliations:
- Krasovskii Institute of Mathematics and Mechanics, Ural Branch
- Issue: Vol 94, No 2 (2016)
- Pages: 563-565
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/224346
- DOI: https://doi.org/10.1134/S1064562416050227
- ID: 224346
Cite item
Abstract
There are some results concerning t-designs in which the number of points in the intersection of two blocks takes less than t values. For example, if t = 2, then the design is symmetric (in such a design, v = b or, equivalently, k = r). In 1974, B. Gross described t-(v, k, l) designs that, for some integer s, 0 < s < t, do not contain two blocks intersecting at exactly s points. Below, it is proved that potentially infinite series of designs from the claim of Gross’ theorem are finite. Gross’ theorem is substantially sharpened.
About the authors
A. A. Makhnev
Krasovskii Institute of Mathematics and Mechanics, Ural Branch
Author for correspondence.
Email: makhnev@imm.uran.ru
Russian Federation, Yekaterinburg, 620219