References 1. Eriksson, H.; Eriksson, K. - Affine Weyl groups as infinite permutations, Electron. J. Combin., 5 (1998), Research Paper 18, 32 pp. 2. Finch, S. - Knots, links and tangles, 2003, http://algo.inria.fr/csolve/knots.pdf 3. Fripertinger, H. - Enumeration and construction in music theory, Diderot Forum on Mathematics and Music Computational and Mathematical Methods in Music, 1999, 179-204 4. Fripertinger, H. - Enumeration in musical theory, Séminaire Lotharingien de Combinatoire

### Roman Wituła

References [1] WITU_LA, R.: The algebraic properties of the convergent and divergent permutations , Filomat (submitted). [2] WITU_LA, R.: The family F of permutations of N, Positivity (submitted). [3] WITU_LA, R.-S_LOTA, D.-SEWERYN, R.: On Erd¨os’ theorem for monotonic subsequences , Demonstr. Math. 40 (2007), 239-259. [4] WITU_LA, R.: On the set of limit points of the partial sums of series rearranged by a given divergent permutation , J. Math. Anal. Appl. 362 (2010), 542

### Niccoló Castronuovo

References [1] R. M. Adin and Y. Roichman, Equidistribution and sign-balance on 321-avoiding permuta- tions, Sém. Lothar. Combin., 51 (2004) Article B51d. [2] E. Barcucci, A. Bernini, L. Ferrari and M. Poneti, A distributive lattice structure con- necting Dyck paths, noncrossing partitions and 312-avoiding permutations, Order, 22 (2005) 311-328. [3] E. Barcucci, A. Del Lungo, E. Pergola and R. Pinzani, ECO: a methodology for the Enumeration of Combinatorial Objects, J. Difference Equ. Appl., 5 (1999) 435

### Eli Bagno, David Garber, Toufik Mansour and Robert Shwartz

multi-colored permutation groups, Electron. J. Combin., 14 (2007) #R24. [5] E. Bagno and D. Garber, On the excedance number of colored permutation groups, Sém. Lothar. Combin., B53f (2006) 17 pp. [6] E. Bagno, D. Garber and T. Mansour, Excedance number for involutions in complex reflection groups, Sém. Lothar. Combin., B56d (2007) 11 pp. [7] M. Bona, Combinatorics of permutations, Chapman and Hall/CRC, Second Edition, 2012. [8] F. Brenti, q-Eulerian polynomials arising from Coxeter groups, European J

### Jean-Luc Baril and Armen Petrossian

References [1] J.-L. Baril, Statistics-preserving bijections between classical and cyclic permutations, Inform. Process. Lett., 113 (2003) 17-22. [2] J.-L. Baril, T. Mansour and A. Petrossian, Equivalence classes of permutations modulo excedances, J. Comb., 5 (2014) 453-469. [3] M. Bona, Combinatorics of permutations, Chapman and Hall/CRC, Second Edition, 2012. [4] E. Deutsch and L. Shapiro, A survey of the Fine numbers, Discrete Math., 241 (2001) 241-265. [5] D. C. Foata and M

### Jean-Luc Baril, Sergey Kirgizov and Armen Petrossian

References [1] E. B abson and E. S teingrímsson , Generalized permutation patterns and a classification of Mahonian statistics , Sém. Lothar. Combin., 44 (2000) Article B44b. [2] E. B arcucci , A. D el L ungo , E. P ergola and R. P inzani , Directed animals, forests and permutations , Discrete Math., 204 (1999) 41–71. [3] J.-L. B aril , T. M ansour and A. P etrossian , Equivalence classes of permutations modulo excedances , J. Comb., 5 (2014) 453–469. [4] J.-L. B aril and A. P etrossian , Equivalence classes of permutations modulo

### Andrzej Krawczyk and Marek Krąpiec

. International Journal of Climatology 1: 345-353, DOI 10.1002/joc.3370010407. Murphy JO, 1991. The downturn in solar activity during solar cycles 5 and 6. Proceedings of the Astronomical Society of Australia 9(2): 330-331. Murphy JO and Veblen TT, 1992. Proxy data from tree ring time series for the eleven year solar cycle. Proceedings of the Astronomical Society of Australia 10: 64-67. Pardo-Igúzquiza E and Rodriguez-Tovar FJ, 2000. The permutation test as a non-parametric method for testing the

### Lin Wang, Heping Ding and Fuliang Yin

Systems, 10 , 1, 1-8. Douglas S. C., Gupta M. (2007), Scaled natural gradient algorithms for instantaneous and convolutive blind source separation , 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 637-640, Honolulu, USA. Hyvarien A., Karhunen J., Oja E. (2001), Independent Component Analysis , John Wiley & Sons, New York. Ikram M. Z., Morgan D. R. (2000), Exploring permutation inconsistency in blind separation of speechsignals in a reverberant environment

### Milan Paštéka and Zuzana Václavíková

## ABSTRACT

In this paper we study the conditions (1), (2) and (3) for the permutations which preserve the weighted density. These conditions are motivated by the conditions of Lévy group, originated in [Levy, P.: Problèmes concrets d’Analyse Fonctionelle. Gauthier Villars, Paris, 1951], and studied in [Obata, N.: Density of natural numbers and Lévy group, J. Number Theory **30 **(1988), 288-297]. In the second part we prove that under some conditions for the sequence of weights, for instance for the logarithmic density, the first two conditions can be launched

### V. U. K. Sastry, N. Ravi Shankar and S. Durga Bhavani

## Abstract

In this paper we have developed a block cipher, wherein the size of the key matrix is 384 bits and the size of the plain text is as large as we choose. The permutation, the interlacing and the iteration introduced in this analysis are found to cause diffusion and confusion efficiently. Hence, the strength of the cipher proves to be remarkable.