An application of the theory of permutations in breaking the Enigma cipher
Marian Rejewski (1980)
Applicationes Mathematicae
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Marian Rejewski (1980)
Applicationes Mathematicae
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Mantaci, Roberto, Rakotondrajao, Fanja (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Raykova, Mariana (2006)
The Electronic Journal of Combinatorics [electronic only]
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Robertson, Aaron (1999)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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R. C. Entriger (1971)
Gaceta Matemática
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Smith, Rebecca (2006)
The Electronic Journal of Combinatorics [electronic only]
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Roman Wituła, Edyta Hetmaniok, Damian Słota (2017)
Open Mathematics
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The aim of this paper is to present some new and essential facts about group 𝒢 generated by the family of convergent permutations, i.e. the permutations on ℕ preserving the convergence of series of real terms. We prove that there exist permutations preserving the sum of series which do not belong to 𝒢. Additionally, we show that there exists a family G (possessing the cardinality equal to continuum) of groups of permutations on ℕ such that each one of these groups is different than...
F. Morley (1893/94)
Bulletin of the New York Mathematical Society
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J. Denés, K. Schermann (1968)
Matematički Vesnik
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Mansour, Toufik (2004)
International Journal of Mathematics and Mathematical Sciences
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Atkinson, M.D., Murphy, M.M., Ruškuc, N. (2005)
The Electronic Journal of Combinatorics [electronic only]
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Zara, Catalin (2003)
The Electronic Journal of Combinatorics [electronic only]
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Martin, Nigel, Stong, Richard (2003)
The Electronic Journal of Combinatorics [electronic only]
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Ewa Romanowicz, Adam Grabowski (2006)
Formalized Mathematics
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We introduce the notion of a permanent [13] of a square matrix. It is a notion somewhat related to a determinant, so we follow closely the approach and theorems already introduced in the Mizar Mathematical Library for the determinant. Unfortunately, the formalization of the latter notion is at its early stage, so we had to prove many very elementary auxiliary facts.