Finite Grassmannian geometries

• Autorzy: Żynel M.
• Języki publikacji: EN

Abstrakty

EN

In the paper we examine the finite case of Grassmannian geometries arising from vector spaces and quadrics. Such geometries are configurations, whose detailed parameters we present. New methods to reduce quadratic forms over finite fields to canonical form, and to count subspaces on a quadric relative to a reflexive form are given.

Słowa kluczowe

EN

Grassmannian geometries

PL

geometria Grassmanniana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2001
• Tom: Vol. 34, nr 1
• Strony: 145--160
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Żynel M.

• Institute of Mathematics University of Białystok ul. Akademicka 2 15-267 Białystok, Poland

Bibliografia

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• [2] Z. Bichara and G. Tallini, On a characterization of Grassmann space representing the h-dimensional subspaces in a projective space, Ann. Discrete Math. 18 (1983), 113-132.
• [3] J. W. P. Hirschfeld, Projective Geometries over Finite Fields, Oxford Mathematical Monographs. Clarendon Press, Oxford, 2nd ed., 1998.
• [4] J. W. P. Hirschfeld and J. A. Thas, General Galois Geometries, Oxford Mathematical Monographs. Clarendon Press, Oxford, 1st ed., 1991.
• [5] R. Lidi and H. Niederreiter, Finite Fields, Addison-Wesley, London, 1983.
• [6] W. Lipski and W. Marek, Analiza Kombinatoryczna, PWN, Warszawa, 1986.
• [7] O. T. O'Meara , Introduction to Quadratic Forms, Springer, Berlin, 1963.
• [8] I. R. Porteous , Topological Geometry, Cambridge University Press, Cambridge, 1981.