Abstract
A valuation is a map from the point set of a point-line geometry \({\mathcal {S}}\) to the set \({\mathbb {N}}\) of nonnegative integers satisfying a number of well-chosen axioms. These axioms are chosen in such a way that these objects are (potentially) useful for classifying certain point-line geometries that contain an isomorphic copy of \({\mathcal {S}}\) as a full subgeometry. Depending on the list of chosen axioms, different “valuation theories” can be developed. The importance of each such theory depends on the successes that can be achieved in classification problems. Valuations have been successfully used for classifying certain near polygons (in particular generalized polygons). They were also useful tools for obtaining a number of other results. The aim of this paper is to survey some of these results.
MSC2000: 51E12, 05B25.
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De Bruyn, B. (2014). The Use of Valuations for Classifying Point-Line Geometries. In: Sastry, N. (eds) Groups of Exceptional Type, Coxeter Groups and Related Geometries. Springer Proceedings in Mathematics & Statistics, vol 82. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1814-2_2
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DOI: https://doi.org/10.1007/978-81-322-1814-2_2
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