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This paper may be considered as a mathematical divertissement as well as a didactical tool for
undergraduate students in a universitary course on algorithms and computation. The wellknown problem of
generating the permutations of a multiset of marks is considered. We define a formal model and an abstract
machine (an extended Turing machine). Then we write an algorithm to compute on that machine the successor
of a given permutation in the lexicographically ordered set of permutations of a multiset. Within the model we
analyze the algorithm, prove its correctness, and show that the algorithm solves the above problem. Then we
describe a slight modification of the algorithm and we analyze in which cases it may result in an improvement of
execution times.
This paper, the ideas in it, and its realization are the work of the first author only.
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