The Polynomial Degree of the Grassmannian {\mathcal G_{\bf 1,}{\bf n,}{\bf 2}}期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The Polynomial Degree of the Grassmannian {\mathcal G_{\bf 1,}{\bf n,}{\bf 2}}

Authors:	R Shaw N A Gordon

Institution:	(1) Department of Mathematics, University of Hull, Hull, HU6 7RX, United Kingdom;(2) Department of Computer Science, University of Hull, Hull, HU6 7RX, United Kingdom

Abstract:	For a subset ψ of PG(N, 2) a known result states that ψ has polynomial degree ≤ r, r≤ N, if and only if ψ intersects every r-flat of PG(N, 2) in an odd number of points. Certain refinements of this result are considered, and are then applied in the case when ψ is the Grassmannian $\mathcal{G}_{1,n,2}\subset PG(N, 2), N = \left( {\begin{array}{l} {n + 1} \\ 2 \\ \end{array} } \right) - 1$ , to show that for n <8 the polynomial degree of $\mathcal{G}_{1,n,2}$ is $\left( {\begin{array}{l} n \\ 2 \\ \end{array}} \right) - 1$ .

Keywords:	polynomial degree subsets of PG(N 2) Grassmannian G₁ n 2
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