An inequality for generalized quadrangles

Payne, Stanley E.

doi:10.1090/S0002-9939-1978-0476547-7

An inequality for generalized quadrangles
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Proc. Amer. Math. Soc. 71 (1978), 147-152 Request permission

Abstract:

Let $\mathcal {S}$ be a generalized quadrangle of order (s, t). Let X and Y be disjoint sets of pairwise noncollinear points of $\mathcal {S}$ such that each point of X is collinear with each point of Y. If $m = |X|$ and $n = |Y|$, then $(m - 1)(n - 1) \leqslant {s^2}$ . When equality holds, severe restrictions are placed on m, n, s, and t.

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