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- W76801763 abstract "Publisher Summary This chapter discusses a coordinatization method for any thick generalized quadrangle (GQ) using a new algebraic structure—that is, a quadratic quaternary ring. A generalized quadrangle is an incidence structure S = (P, L, I) with point set P and line set L, satisfying the following axioms: (1) each point is incident with 1 + t lines and two distinct points are incident with at most one line, (2) each line is incident with 1 + s points and two distinct lines are incident with at most one point; (3) if P is a point and L is aline not incident with P , then there is a unique pair. For the duality for GQ, it is assumed that the dual of a given definition or theorem has also been given implicitly. One of the most powerful concepts in the modern theory of projective planes is that of coordinatization. The proposed method of coordinatization works in the case of generalized n-gons as well. The theory of quadratic quaternary rings is also crucial in describing an affine building in terms of its (infinite) generalized quadrangle at infinity." @default.
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- W76801763 date "1988-01-01" @default.
- W76801763 modified "2023-09-24" @default.
- W76801763 title "Coordinatization of Generalized Quadrangles" @default.
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- W76801763 doi "https://doi.org/10.1016/s0167-5060(08)70239-5" @default.
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