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In mathematics, a Buekenhout geometry or diagram geometry is a generalization of projective space, Tits buildings, and several other geometric structures, introduced by . ==Definition== A Buekenhout geometry consists of a set ''X'' whose elements are called "varieties", with a symmetric reflexive relation on ''X'' called "incidence", together with a function τ called the "type map" from ''X'' to a set Δ whose elements are called "types" and whose size is called the "rank". A flag is a subset of ''X'' such that any two elements of the flag are incident. The Buekenhout geometry has to satisfy the following axiom: *Every flag is contained in a flag with exactly one variety of each type. Example: ''X'' is the linear subspaces of a projective space with two subspaces incident if one is contained in the other, Δ is the set of possible dimensions of linear subspaces, and the type map takes a linear subspace to its dimension. A flag in this case is a chain of subspaces, and each flag is contained in a so-called complete flag. If ''F'' is a flag, the residue of ''F'' consists of all elements of ''X'' that are not in ''F'' but are incident with all elements of ''F''. The residue of a flag forms a Buekenhout geometry in the obvious way, whose type are the types of ''X'' that are not types of ''F''. A geometry is said to have some property residually if every residue of rank at least 2 has the property. In particular a geometry is called residually connected if every residue of rank at least 2 is connected (for the incidence relation). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Buekenhout geometry」の詳細全文を読む スポンサード リンク
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