Equal moments division of a set
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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 $m\le 8$ and $N\le 167$, 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 $m\le 6$.References
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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
- Received by editor(s): March 19, 2007
- Received by editor(s) in revised form: May 23, 2007
- Published electronically: January 29, 2008
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 77 (2008), 1695-1712
- MSC (2000): Primary 11B83, 12D10; Secondary 94B05, 11Y99
- DOI: https://doi.org/10.1090/S0025-5718-08-02072-3
- MathSciNet review: 2398788