Disjoint subsets of integers having a constant sum

نویسندگان

  • Kiyoshi Ando
  • Severino V. Gervacio
  • Mikio Kano
چکیده

We prove that for position 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 ≤ m ≤ n(n+ 1)/(2k).

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Disjoint odd integer subsets having a constant odd sum

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.

متن کامل

On the Complexity of Variations of Equal Sum Subsets

The Equal Sum Subsets problem, where we are given a set of positive integers and we ask for two nonempty disjoint subsets such that their elements add up to the same total, is known to be NP-hard. In this paper we give (pseudo-)polynomial algorithms and/or (strong) NP-hardness proofs for several natural variations of Equal Sum Subsets. Among others we present (1) a framework for obtaining NP-ha...

متن کامل

On sequences of positive integers containing no p terms in arithmetic progression

We use topological ideas to show that, assuming the conjecture of Erdös [4] on subsets of positive integers having no p terms in arithmetic progression (A. P.), there must exist a subset Mp of positive integers with no p terms in A. P. with the property that among all such subsets, Mp maximizes the sum of the reciprocals of its elements.

متن کامل

Indecomposable Tilings of the Integers with Exponentially Long Periods

Let A be a finite multiset of integers. A second multiset of integers T is said to be an A-tiling of level d if every integer can be expressed in exactly d ways as the sum of an element of A and of an element of T . The set T is indecomposable if it cannot be written as the disjoint union of two proper subsets that are also A-tilings. In this paper we show how to construct indecomposable tiling...

متن کامل

Balanced Degree-Magic Labelings of Complete Bipartite Graphs under Binary Operations

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete Mathematics

دوره 82  شماره 

صفحات  -

تاریخ انتشار 1990