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In this paper we give an algorithm to generate all distributions of distinguishable objects to bins without repetition. Our algorithm generates each distribution in constant time. To the best of our knowledge, our algorithm is the first algorithm which generates each solution in O(1) time in the ordinary sense. As a byproduct of our algorithm, we obtain a new algorithm to enumerate all multiset partitions when the number of partitions is fixed and the partitions are numbered. In this case, the algorithm generates each multiset partitions in constant time (in the ordinary sense). Finally, we extend the algorithm to the case when the bins have priorities associated with them. Overall space complexity of the algorithm is O(mklgn), where there are m bins and the objects fall into k different classes. In a companion paper, the generation of all distributions of identical objects to bins is also considered. [ABSTRACT FROM AUTHOR]

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over. [ABSTRACT FROM PUBLISHER]

A successive method of descending degree has been presented by Guo, Liu and Jia in 2002 to judge whether or not a matrix is a generalized diagonally dominant matrix. In this paper, an alternative approach and comments on one of their examples are provided. Numerical examples are given to illustrate the algorithm processing. [ABSTRACT FROM AUTHOR]