In this paper, we show that the algebra of permutation group is one of the inherent structures of reversible logic for quantum computation. In this venture, we discuss necessary properties of cycle ...

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ABSTRACT: In combinatorics, permutations are important objects with many operations. In this paper, we define a coupling product on permutations and prove that the space spanned by permutations is a ...

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Abstract: We construct an explicit Hopf algebra isomorphism from the algebra of heap-ordered trees to that of quasi-symmetric functions, generated by formal permutations, which is a lift of the ...

Hello, wrong number At the heart of machine learning are patterns, and patterns are all about counting, so it's important to make sure we are counting the correct items in the correct way.

There is an ideal random number generator, which given a positive integer M can generate any real number between 0 to M, and probability density function is uniform in [0, M]. Given two numbers A and ...

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