Algorithms
Generations of permutations with non-unique elements
ACM SIGNUM Newsletter
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Algorithm 264: Map of partitions into integers
Communications of the ACM
Algorithm 262: Number of restricted partitions of N
Communications of the ACM
Algorithm 95: Generation of partitions in part-count form
Communications of the ACM
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
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A systematic method to deal with the interrelations of systems with multi-index quantities (random variables) is proposed. The method differs of the well-known Polykays. An application of the theoretical results here presented is the calculation of the moments of the sample variance for general populations in a direct way. The main advantage of the proposed methodology is that no conversion formulae and other complicated Polykays rules are needed. However, the proposed method is compatible with Polykays philosophy and conversion formulae and multiplication rules can be derived by using the theoretical results of this work. For practical purposes, two algorithms for the calculation of the moments of the sample variance are proposed.