THE TRIPLE AND QUADRUPLE COMPLETE PARTITIONS OF  INTEGERS

P Geetha; A Gnanam

doi:10.48165/

Authors

P Geetha Assistant Professor, Department of Mathematics, Periyar Maniammai Institute of Science & Technology, Periyar Nagar, Vallam, Thanjavur, Tamil Nadu 613403, India.
A Gnanam Assistant Professor, Department of Mathematics, Government Arts College, Thuvakkudimalai, Trichy, Tamil Nadu 620022, India

DOI:

https://doi.org/10.48165/

Keywords:

Partitions, Complete Partitions, Double complete partitions

Abstract

Complete partitions are introduced by S.K. Park [6] and the representation of a positive integer in terms of a sum of smaller numbers with certain conditions has been developed by Mac Mahon [5] in perfect partitions. This paper presents the concepts of complete partition, double complete partition and an attempt is made for the triple and quadruple complete partitions of integers.

References

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Niven, Ivan, Zuckerman, Herbert S. and Montgomery, Hugh L. (1991). An Introduction to the theory of Numbers, 5th Edition, John Wiley & Sons, Inc. New York.

Andrews, G.E. (1976). The Theory of Partitions, Encyclopedia of Mathematics and Its Applications. Vol.2. Reading, Mass.: Addison-Wesley, 1976.

Mac Mahon, P.A. (1975). Combinatory Analysis, Vols I and II, Cambridge Univ. Press, Cambridge, 1975, 1916 (reprinted, Chelsea, 1960).

Park, Seung Kyung (1996). Complete Partitions, Yonsei University, Seoul 120 – 749, Korea. [7] Lee, Hokyu and Park, Seung Kyung (2002). The Double Complete Partitions of Integers, Commun. Korean Math. Soc., 17, No.3, 431 – 437.