منابع مشابه
Base subsets of polar Grassmannians
Let ∆ be a thick building of type Xn = Cn,Dn. Let also Gk be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write Gk for the corresponding shadow space of type Xn,k. Every bijective transformation of Gk preserving the class of base subsets (the shadows of apartments) is a collineation of Gk, and it is induced by a collineation of Π if n 6= 4...
متن کاملBase subsets of symplectic Grassmannians
Let V and V ′ be 2n-dimensional vector spaces over fields F and F ′. Let also : V × V → F and ′: V ′ × V ′ → F ′ be non-degenerate symplectic forms. Denote by and ′ the associated (2n − 1)-dimensional projective spaces. The sets of kdimensional totally isotropic subspaces of and ′ will be denoted by Gk and G ′ k , respectively. Apartments of the associated buildings intersect Gk and G ′ k by so...
متن کاملFinite Subsets of Grassmannians
Let A be a subvariety of affine space A whose irreducible components are d-dimensional linear or affine subspaces of A. Denote by D(A) ⊂ N the set of exponents of standard monomials ofA. Using the Hilbert function, we show thatD(A) contains as many subspaces of dimension d as A contains irreducible components. We refine this result in various ways. Firstly, we specify the directions into which ...
متن کاملOn hyperovals of polar Grassmannians
A hyperoval of a point-line geometry is a nonempty set of points meeting each line in either 0 or 2 points. In this paper, we study hyperovals in line Grassmannians of finite polar spaces of rank 3, hereby often imposing some extra regularity conditions. We determine an upper bound and two lower bounds for the size of such a hyperoval. If equality occurs in one of these bounds, then there is an...
متن کاملPolar Grassmannians and their Codes
We present a concise description of Orthogonal Polar Grassmann Codes and motivate their relevance. We also describe efficient encoding and decoding algorithms for the case of Line Grassmannians and introduce some open problems.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2007
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2007.02.003