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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Robertson, Aaron (1999)
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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Lewis, Joel Brewster (2009)
The Electronic Journal of Combinatorics [electronic only]
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Paweł Klinga (2016)
Colloquium Mathematicae
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We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.
F. Morley (1893/94)
Bulletin of the New York Mathematical Society
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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...
Barcucci, Elena, Del Lungo, Alberto, Pergola, Elisa, Pinzani, Renzo (2000)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Augustine Munagi (2014)
Open Mathematics
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The study of parity-alternating permutations of {1, 2, … n} is extended to permutations containing a prescribed number of parity successions - adjacent pairs of elements of the same parity. Several enumeration formulae are computed for permutations containing a given number of parity successions, in conjunction with further parity and length restrictions. The objects are classified using direct construction and elementary combinatorial techniques. Analogous results are derived for circular...
Mantaci, Roberto, Rakotondrajao, Fanja (2001)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Bóna, Miklós (1998)
The Electronic Journal of Combinatorics [electronic only]
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Smith, Rebecca (2006)
The Electronic Journal of Combinatorics [electronic only]
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Mansour, Toufik (2004)
International Journal of Mathematics and Mathematical Sciences
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Martin, Nigel, Stong, Richard (2003)
The Electronic Journal of Combinatorics [electronic only]
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