منابع مشابه
Schubert unions in Grassmann varieties
We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study the linear spans of, and in case of positive characteristic, the number of Fq-rational points on such unions. Moreover we study a geometric duality of such unions, and give a combinatorial interpretation of this duality. We discuss the ma...
متن کاملGrassmann Codes and Schubert Unions
— We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study such sets in detail, and give applications to coding theory, in particular for Grassmann codes. For l = 2 much is known about such Schubert unions with a maximal number of Fq-rational points for a given spanning dimension. We study the ...
متن کاملIdeals Defining Unions of Matrix Schubert Varieties
This note computes a Gröbner basis for the ideal defining a union of matrix Schubert varieties. Moreover, the theorem presented will work for any union of schemes defined by northwest rank conditions. This provides a means of intersecting a large class of determinantal ideals. Introduction We compute a Gröbner basis for the ideal defining a union of schemes defined by northwest rank conditions ...
متن کاملSCHUBERT UNIONS AND CODES ON l - STEP FLAG VARIETIES
— In Section 1 we define and study Schubert unions on l-step flag varieties. This has previously been done in the Grassmann case, i.e., the l = 1 case, by Hansen, Johnsen and Ranestad [7]. In Section 2 we study the algebraic codes given by mapping l-step flag varieties into projective space. This subject has also been treated in the Grassmann case previously (see p. 52). Résumé (Unions de cellu...
متن کاملHigher weights of Grassmann codes in terms of properties of Schubert unions
We describe the higher weights of the Grassmann codes G(2, m) over finite fields Fq in terms of properties of Schubert unions, and in each case we determine the weight as the minimum of two explicit polynomial expressions in q.
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2007
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2007.06.003