منابع مشابه
7 on Tight Projective Designs
It is shown that among all tight designs in FP n = RP 1 , where F is R or C, or H (quaternions), only 5-designs in CP 1 [14] have irrational angle set. This is the only case of equal ranks of the first and the last irreducible idempotent in the corresponding Bose-Mesner algebra.
متن کاملOn Tight Spherical Designs
Let X be a tight t-design of dimension n for one of the open cases t = 5 or t = 7. An investigation of the lattice generated by X using arithmetic theory of quadratic forms allows to exclude infinitely many values for n.
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A Gaussian t-design is defined as a finite set X in the Euclidean space Rn satisfying the condition: 1 V (Rn ) ∫ Rn f (x)e −α2||x ||2 dx = u∈X ω(u) f (u) for any polynomial f (x) in n variables of degree at most t , here α is a constant real number and ω is a positive weight function on X . It is easy to see that if X is a Gaussian 2e-design in Rn , then |X | ≥ (n+e e ) . We call X a tight Gaus...
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We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning the tight closure of a primary ideal in a two-dimensional graded domain.
متن کاملOn antipodal Euclidean tight ( 2 e + 1 ) - designs
Neumaier and Seidel (1988) generalized the concept of spherical designs and defined Euclidean designs in Rn . For an integer t , a finite subset X of Rn given together with a weight function w is a Euclidean t-design if ∑p i=1 w(Xi ) |Si | ∫ Si f (x)dσi (x) = ∑ x∈X w(x) f (x) holds for any polynomial f (x) of deg( f ) ≤ t , where {Si , 1 ≤ i ≤ p} is the set of all the concentric spheres centere...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2008
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-008-9240-4