VALUATIONS OF NEAR POLYGONS

BART DE BRUYN; PIETER VANDECASTEELE

doi:10.1017/S0017089505002582

Abstract

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We introduce the notion of valuation of a dense near polygon. The valuations of a dense near polygon $F$ describe the possible relations between a point of a dense near polygon $\cS$ and any geodetically closed sub near polygon of $\cS$ isomorphic to $F$. Several nice properties of valuations are given and several classes of these objects are defined. Valuations are an important tool for classifying dense near polygons.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

De Bruyn, Bart and Vandecasteele, Pieter 2005. Valuations and hyperplanes of dual polar spaces. Journal of Combinatorial Theory, Series A, Vol. 112, Issue. 2, p. 194.

De Bruyn, Bart 2007. A characterization of the SDPS-hyperplanes of dual polar spaces. European Journal of Combinatorics, Vol. 28, Issue. 3, p. 705.

De Bruyn, Bart 2007. Dense near octagons with four points on each line, II. advg, Vol. 7, Issue. 2, p. 191.

De Bruyn, Bart and Vandecasteele, Pieter 2007. The classification of the slim dense near octagons. European Journal of Combinatorics, Vol. 28, Issue. 1, p. 410.

De Bruyn, Bart 2007. Valuations of glued near hexagons. Journal of Combinatorial Designs, Vol. 15, Issue. 1, p. 35.

De Bruyn, B. 2008. Isometric full embeddings of DW(2n−1,q) into DH(2n−1,q2). Finite Fields and Their Applications, Vol. 14, Issue. 1, p. 188.

De Bruyn, Bart and Pralle, Harm 2008. The hyperplanes of the near hexagon on the 2-factors of the complete graph K8. Discrete Mathematics, Vol. 308, Issue. 23, p. 5656.

Bruyn, Bart De 2008. Two new classes of hyperplanes of the dual polar space DH(2n-1,4) not arising from the Grassmann embedding. Linear Algebra and its Applications, Vol. 429, Issue. 8-9, p. 2030.

De Bruyn, Bart 2009. The uniqueness of the SDPS-set of the symplectic dual polar space DW(4n−1,q), n≥2. European Journal of Combinatorics, Vol. 30, Issue. 4, p. 911.

De Bruyn, Bart and Shpectorov, Sergey 2010. The Hyperplanes of the U 4(3) Near Hexagon. Graphs and Combinatorics, Vol. 26, Issue. 5, p. 647.

De Bruyn, Bart 2010. On geometric SDPS-sets of elliptic dual polar spaces. Journal of Combinatorial Theory, Series A, Vol. 117, Issue. 5, p. 528.

De Bruyn, B. and Vandecasteele, P. 2010. The valuations of the near octagon G4. Discrete Mathematics, Vol. 310, Issue. 4, p. 755.

De Bruyn, Bart 2011. Dense Near Octagons with Four Points on Each Line, III. Annals of Combinatorics, Vol. 15, Issue. 1, p. 19.

De Bruyn, Bart 2012. The Hyperplanes of the Glued Near Hexagon $${Q(5, 2) \otimes Q(5, 2)}$$. Annals of Combinatorics, Vol. 16, Issue. 4, p. 661.

De Bruyn, Bart 2013. Polygonal valuations. Discrete Mathematics, Vol. 313, Issue. 1, p. 84.

De Bruyn, Bart 2013. Isometric embeddings of the near polygonsHnandGninto dual polar spaces. Discrete Mathematics, Vol. 313, Issue. 12, p. 1312.

De Bruyn, Bart 2014. Groups of Exceptional Type, Coxeter Groups and Related Geometries. Vol. 82, Issue. , p. 27.

De Bruyn, Bart 2014. Isometric Embeddings Between the Near Polygons $${\mathbb{H}_n}$$ H n and $${\mathbb{G}_n}$$ G n. Annals of Combinatorics, Vol. 18, Issue. 2, p. 265.

De Bruyn, Bart 2015. The uniqueness of a certain generalized octagon of order (2,4). Discrete Mathematics, Vol. 338, Issue. 12, p. 2125.

Bishnoi, Anurag and De Bruyn, Bart 2016. On Semi-Finite Hexagons of Order (2, t) Containing a Subhexagon. Annals of Combinatorics, Vol. 20, Issue. 3, p. 433.

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VALUATIONS OF NEAR POLYGONS

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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VALUATIONS OF NEAR POLYGONS

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