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THE DOUBLE-COMPLETE PARTITIONS OF INTEGERS

  • Lee, Ho-Kyu (Department of Mathematics Ewha Womans University) ;
  • Park, Seung-Kyung (Department of Mathematics Yonsei University)
  • Published : 2002.07.01

Abstract

Representing a positive integer in terms of a sum of smaller numbers with certain conditions has been studied since MacMahon [5] pioneered perfect partitions. The complete partitions is in this category and studied by the second author[6]. In this paper, we study complete partitions with more specified completeness, which we call the double-complete partitions.

Keywords

complete partition;double complete partition

References

  1. Fibonacci Quart v.36 Complete Partitions S. Park
  2. Cambridge University Press v.1;2 Combinatory Analysis P. A. MacMahon
  3. Amer. Math. Monthly v.67 Problem E 1424 V. E. Hoggatt;C. King
  4. Discrete Math. v.183 The r-complete Partitions https://doi.org/10.1016/S0012-365X(97)00177-5
  5. Amer. Math. Monthly v.68 Note on complete sequences of integers J. L. Brown https://doi.org/10.2307/2311150
  6. preprint The r-perfect Partitions H. Lee;S. Park
  7. preprint The generalizations of Zeckendorf Theorem