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A large index theorem for orthogonal arrays, with bounds

โœ Scribed by Steven J. Rosenberg

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
131 KB
Volume
137
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

It is shown that for fixed v,k, and t, an orthogonal array A, (v,k, 2) exists for ~2k-21) 2k-t.

Information on the number of orthogonal arrays with given parameters, as a function of 2, is also obtained.

In this paper v,k, and t will be fixed integers satisfying v>~2 and 1 <~t<~k. Let Iv] denote the set {1,2 ..... v} and let Iv] k denote the set {a =(al, a2, ... ,ak): a~ [v] Vi}. For positive integers 2, we define an orthooonal array At(v,k,2) to be a function A: [v] k ~ [~o (nonnegative integers) such that given any t-set I ~_ [k] and any element a~ [v] k, we have ~ A ( x ) = 2 , where the sum is over those x in [v] k such that xi=ai VieI. Ray-Chaudhuri and Singhi [1] have shown that an At(v, k, 2) always exists for

๐Ÿ“œ SIMILAR VOLUMES

A Lower Bound for Orthogonal Polynomials
A Lower Bound for Orthogonal Polynomials with an Application to Polynomial Hypergroups
โœ R. Szwarc ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 173 KB

We give a lower bound for solutions of linear recurrence relations of the form \(z a_{n}=\sum_{k=n-N}^{n+N} \alpha_{k, n} a_{k}\), whenever \(z\) is not in the \(P^{P}\)-spectrum of the corresponding banded operator. In particular if \(P_{n}\) are polynomials orthonormal with respect to a measure \(