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Enumeration of the distinct shuffles of permutations [PDF]
Discrete Mathematics & Theoretical Computer Science, 2009 A shuffle of two words is a word obtained by concatenating the two original words in either order and then sliding any letters from the second word back past letters of the first word, in such a way that the letters of each original word remain spelled ...
Camillia Smith Barnes
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Permutations by Interchanges [PDF]
The Computer Journal, 1963 Methods for obtaining all possible permutations of a number of objects, in which each permutation differs from its predecessor only by the interchange of two of the objects, are discussed. Details of two programs which produce these permutations are given, one allowing a specified position to be filled by each of the objects in a predetermined order ...
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Partitioned Cacti: a Bijective Approach to the Cycle Factorization Problem [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 In this paper we construct a bijection for partitioned 3-cacti that gives raise to a new formula for enumeration of factorizations of the long cycle into three permutations with given number of cycles.
Gilles Schaeffer, Ekaterina Vassilieva
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Determinant of binary circulant matrices
Special Matrices, 2019 This article gives a closed-form expression for the determinant of binary circulant matrices.
Hariprasad M.
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Homogeneous Permutations [PDF]
The Electronic Journal of Combinatorics, 2002 There are just five Fraïssé classes of permutations (apart from the trivial class of permutations of a singleton set); these are the identity permutations, reversing permutations, composites (in either order) of these two classes, and all permutations. The paper also discusses infinite generalisations of permutations, and the connection with Fraïssé's ...
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Profiles of Permutations [PDF]
The Electronic Journal of Combinatorics, 2009 This paper develops an analogy between the cycle structure of, on the one hand, random permutations with cycle lengths restricted to lie in an infinite set $S$ with asymptotic density $\sigma$ and, on the other hand, permutations selected according to the Ewens distribution with parameter $\sigma$.
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Pattern classes of permutations via bijections between linearly ordered sets [PDF]
, 2008 A pattern class is a set of permutations closed under pattern involvement or, equivalently, defined by certain subsequence avoidance conditions. Any pattern class X which is atomic, i.e.
Ruškuc, Nik +2 more
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Permutation Reconstruction [PDF]
The Electronic Journal of Combinatorics, 2006 In this paper, we consider the problem of permutation reconstruction. This problem is an analogue of graph reconstruction, a famous question in graph theory. In the case of permutations, the problem can be stated as follows: In all possible ways, delete $k$ entries of the permutation $p=p_1p_2p_3...p_n$ and renumber accordingly, creating $n \choose k$
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General Diffusion Analysis: How to Find Optimal Permutations for Generalized Type-II Feistel Schemes
IACR Transactions on Symmetric Cryptology, 2019 Type-II Generalized Feistel Schemes are one of the most popular versions of Generalized Feistel Schemes. Their round function consists in applying a classical Feistel transformation to p sub-blocks of two consecutive words and then shifting the k = 2p ...
Victor Cauchois +2 more
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Permutation Statistics of Indexed Permutations
European Journal of Combinatorics, 1994 The definitions of descent, exceedance, major index, inversion index and Denert's statistic for the elements of the symmetric group \({\mathcal S}_ d\) are generalized to indexed permutations, i.e. the elements of the group \(S^ n_ d:=\mathbb{Z}_ n\wr{\mathcal S}_ d\), where \(\wr\) is the wreath product with respect to usual action of \({\mathcal S}_ ...
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