The Sextuple Complete Partitions of Integers
DOI:
https://doi.org/10.12723/mjs.sp1.10Keywords:
Integers, Compositions, Partitions, Complete PartitionsAbstract
This paper presents the concepts of sextuple (6 – tuple) complete partitions of integers and an attempt has been given for the theorem based on the last part of sextuple complete partitions of integers.
References
Oystein J. Rodseth, Journal of integer sequences, Vol. 10 (2007).
S. K. Park, Complete Partitions, Fibonacci Quart., to appear.
P. A. Mac Mahon, Combinatory Analysis, Vols I and II, Cambridge Univ. Press, Cambridge, 1975, 1916 (reprinted, Chelsea, 1960).
V. E. Hoggatt & C. King, “Problem E 1424” Amer. Math. Monthly 67 (1960) : 593.
J. L. Brown, Note on Complete sequences of Integers, Amer. Math. Monthly 68 (1961).
George E. Andrews, Number Theory, W. B. Saunders Company, London.
Hokyu Lee and Seung Kyung Park, The Double Complete Partitions of Integers, Commun. Korean Math. Soc. 17(2002), No.3, pp. 431 – 437.
Tom M. Apostol, Introduction to Analytic Number theory, Springer – Verlag, New York Heidelberg Berlin, 1976.
Ivan Niven, Herbert S. Zuckerman, Hugh L. Montgomery, An Introduction to the theory of Numbers, 5th Edition, John Wiley & Sons, Inc. New York.
G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and Its Applications. Vol.2. Reading, Mass.: Addison-Wesley, 1976.
Geetha. P, Gnanam. A, The Triple and Quadruple Complete Partitions of Integers, Bulletin of Pure and Applied
Sciences, Vol. 38E (Math & Stat.), No. 1, 2019, P.356-358. Print version ISSN 0970 6577, Online version ISSN 2320 3226,
DOI: 10.5958/23203226.2019.00038.9
Agarwal A. K and M. V. Subbarao, Some properties of perfect partitions, Indian J. pure appl. Math., 22(9) : 737 – 743,
September 1991.
Agarwal A. K, Padmavathamma, and M. V. Subbarao, Partition theory, Atma Ram & Sons, Chandigarh, 2005.
Ahlgren S. and Boylan M., Arithmetic properties of the partition function, Invent. Math. 153(2003), 487 – 502.
Seung Kyung Park,The r-complete Partitions, Discrete Mathematics 183 (1998): 293-297.
Hokyu Lee, The r – subcomplete partitions, Ewha Womans University, Seoul 120 – 750, Korea, April 2002.
Ncvillc Robbins, On partition functions and Divisor sums, Journal of integer sequences, Vol. 5, 2002.
James A. Sellers, Andrew V. Sills and Gary L. Mullen, Bijections and Congruences for Generalizations of Partition identities of Euler and Guy, The electronic journal of combinatorics, 2004.
James A. Sellers, Partitions Excluding specific polygonal numbers as parts, Journal of integer sequences, Vol. 7(2004).
Hodyu Lee, Double perfect partitions, Discrete Mathematics 306 (2006), 519 – 525.
Oystein J. Rodseth, Enumeration of M – partitions, Discrete Mathematics, 2006.
Oystein J. Rodseth, Minimal r – complete partitions, Journal of integer sequences, Vol. 10 (2007).
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