The Polynomial Degree of the Grassmannian G 1,n,2

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For a subset ψ of PG(N, 2) a known result states that ψ has polynomial degree ≤ r, rN, 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 G1,n,2 ⊂PG(N,2), N=(n+1/2)− 1 to show that for n <8 the polynomial degree of G1,n,2 is (n/2)−1.

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