Integer partitions revisited using multisets and binary matrices
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DOI:
https://doi.org/10.26637/MJM0801/0047Abstract
In this paper, partition of a positive integer is represented as a multiset and binary matrix. New formulae and theorems of integer partition are developed by using the results of multiset theory and the binary matrix concept. Few properties of this binary matrix are found. Some well known theorems of integer partitions are proved using this binary matrix and multiset representations.
Keywords:
Multisets, Integer partitions, partitions,Conjugate of a partition, Self Conjugate, Binary matrix, 1-matriMathematics Subject Classification:
Mathematics- Pages: 282-287
- Date Published: 01-01-2020
- Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)
H. L. Alder, Partition Identities - From Euler to the Present, Amer. Math Monthly, 76(1969), 733-746.
G. E. Andrews, The Theory of Partitions, Encyclopedia of Math and Its Applications , 2(1985), 11-22.
Edward A.Bender, Partitions of Multisets, Discrete mathematics, (1974), 301-311.
Wayne D. Blizard, Multiset theory, Notre dame Journal of Formal Logic,30(1989), 36-66.
Wayne D. Blizard, The Developement of Multiset theory , Modern Logic , 1(1991), 319-352.
Chris Brink, Multisets and the Algebra of Relevance logic, Non-Classical Logic, 5(1988), 75-95.
C. S. Calude , G. Paun, G. Rozenberg and A. Salomaa, Mathematics of Multisets, Springer Verlag, (2001), 347358.
Manosij Ghosh Dastidar1 and Sourav Sen Gupta, Generalization of a few results in integer partitions, Notes on Number Theory and Discrete Mathematics , 19(2013), 69-76
K. P. Girish and Sunil Jacob John, Relations and functions in multiset context, Information Sciences, 179(2009), 758-768.
Alexander D.Healy, Partition Identities, www.alexhealy.net/papers/math 192.pdf (2001).
D. Singh , A. M. Ibrahim, T. Yohanna and J. N. Singh ,An overview of the application of multise, Novi Sad J. Math, 37(2007), 73-92.
N.J. Wildberger, A new look at multisets, School of Mathematics UNSW Sydney 2053, (2003).
Herbert S. Wilf, Lectures on Integer Partitions, Delivered at the University of Victoria Canada, (2000).
R. R. Yager, On the theory of bags, International Journal of General Systems, 13(1986), 23-37.
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