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Mathematics of Computation

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Equal moments division of a set


Author: Shahar Golan
Journal: Math. Comp. 77 (2008), 1695-1712
MSC (2000): Primary 11B83, 12D10; Secondary 94B05, 11Y99
Published electronically: January 29, 2008
MathSciNet review: 2398788
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Abstract: Let $ N_q^{*}(m)$ be the minimal positive integer $ N$, for which there exists a splitting of the set $ [0,N-1]$ into $ q$ subsets, $ S_0$, $ S_1$, ..., $ S_{q-1}$, whose first $ m$ moments are equal. Similarly, let $ m_q^{*}(N)$ be the maximal positive integer $ m$, such that there exists a splitting of $ [0,N-1]$ into $ q$ subsets whose first $ m$ moments are equal. For $ q=2$, these functions were investigated by several authors, and the values of $ N_2^{*}(m)$ and $ m_2^{*}(N)$ have been found for $ m\le8$ and $ N\le167$, respectively. In this paper, we deal with the problem for any prime $ q$. We demonstrate our methods by finding $ m_3^*(N)$ for any $ N<90$ and $ N_3^*(m)$ for $ m\le 6$.


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Additional Information

Shahar Golan
Affiliation: Department of Computer Science, Ben-Gurion University of the Negev, POB 653, Beer-Sheva 84105 Israel
Email: golansha@cs.bgu.ac.il

DOI: https://doi.org/10.1090/S0025-5718-08-02072-3
Keywords: Littlewood polynomials, spectral-null code, antenna array
Received by editor(s): March 19, 2007
Received by editor(s) in revised form: May 23, 2007
Published electronically: January 29, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.