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The spectrum of support sizes for threefold triple systems

โœ Scribed by Charles J. Colbourn; Ebadollah S. Mahmoodian

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
656 KB
Volume
83
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

The spectrum of possible numbers of distinct blocks in a threefold triple system of order u is determined.

Let m, = [u(u -1)/6]. A threefold triple system with u = 1, 3 (mod 6) elements can have any number of distinct blocks from, and only from, {m,, m, + 4, m, +6, m, + 7;.., 3m,} provided u # 3, 7, 9. A threefold triple system with u = 5 (mod 6) elements can have any number of distinct blocks from, and only from, {m, + 7, m, + 10, m, + 11, .

,3m, + 1).

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