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Some combinatorics of multisets

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The purpose of this paper is to delineate some insights into the concept of multisets along with a couple of combinatorial results related to multisets. The paper indicates that a general formula needs to be worked out for determining the cardinality of the 'Set' (whose elements may be multisets but do not repeat) of all multisubsets of a finite multiset [x, y, z,…]m, p, t, … in which x occurs at most m times, y occurs at most p times, and so on. It outlines some directions provided in the literature and points out that they all turn out to be inefficient. Finally, a relatively more efficient formula to this effect is provided along with a remark that the problem needs further vindication.

Document Type: Research Article


Affiliations: 1: Professor of Pure Mathematics Mathematics Department Faculty of Science Ahmadu Bello University Zaria Nigeria, Email: 2: Department of Mathematics and Computer Science Barry University 11300 Northeast second Avenue Miami Shores FL 33161 USA, Email:

Publication date: July 1, 2003

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