On Euclidean tight 4-designs
نویسندگان
چکیده
منابع مشابه
Tight Gaussian 4-Designs
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...
متن کاملOn the strong non-rigidity of certain tight Euclidean designs
We study the non-rigidity of Euclidean t-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean t-designs. We show that certain tight Euclidean t-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isom...
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...
متن کاملOn Euclidean t-designs
A Euclidean t-design, as introduced by Neumaier and Seidel (1988), is a finite set X ⊂ Rn with a weight function w : X → R+ for which
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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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 2006
ISSN: 0025-5645
DOI: 10.2969/jmsj/1156342038