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Disjoint subsets of integers having a constant sum

โœ Scribed by Kiyoshi Ando; Severino Gervacio; Mikio Kano

Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
262 KB
Volume
82
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

We prove that for positive integers n, m and k, the set (1, 2, . , n} of integers contains k disjoint subsets having a constant sum m if and only if 2k -1 G m c n(n + 1)/(2k).

๐Ÿ“œ SIMILAR VOLUMES

Disjoint odd integer subsets having a co
Disjoint odd integer subsets having a constant even sum
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We prove that for positive integers n and k and a positive even integer m, the odd integer set {1,3,5 ..... 2n-l} contains k disjoint subsets having a constant sum m if and only if 4k<~m<~n2/k, n2-mk#2 and either m#4n-2 or n#4k.

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We prove that for positive k, n and m, the set { 1,3, . ,2n -1) of odd integers contains k disjoint subsets having a constant odd sum m if and only if 9(k-1)Cm <2n-1, or 9k<m<n2/k and n2-mk#2.