On 2-designs |
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| Authors: | P Erdös Joel C Fowler Vera T Sós Richard M Wilson |
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| Affiliation: | Hungarian Academy of Sciences Hungary;California Institute of Technology, Pasadena, California 91125 USA;Bell Laboratories, Murray Hill, New Jersey 07974 USA;California Institute of Technology, Pasadena, California 91125 USA |
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| Abstract: | Denote by Mv the set of integers b for which there exists a 2-design (linear space) with v points and b lines. Mv is determined as accurately as possible. On one hand, it is shown for v > v0 that Mv contains the interval [v + p + 1, v + p + q ? 1]. On the other hand for v of the form p2 + p + 1 it is shown that the interval [v + 1, v + p ? 1] is disjoint from Mv; and if v > v0 and p is of the form q2 + q, then an additional interval [v + p + 1, v + p + q ? 1] is disjoint from Mv. |
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