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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An inequality for generalized quadrangles


Author: Stanley E. Payne
Journal: Proc. Amer. Math. Soc. 71 (1978), 147-152
MSC: Primary 05B25
DOI: https://doi.org/10.1090/S0002-9939-1978-0476547-7
MathSciNet review: 0476547
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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 = \vert X\vert$ and $ n = \vert Y\vert$, 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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DOI: https://doi.org/10.1090/S0002-9939-1978-0476547-7
Keywords: Generalized quadrangles, Rayleigh quotient, incidence matrix
Article copyright: © Copyright 1978 American Mathematical Society

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