Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

Generating trees for permutations avoiding generalized patterns

We construct generating trees with with one, two, and three labels for some classes of permutations avoiding generalized patterns of length 3 and 4. These trees are built by adding at each level an entry to the right end of the permutation, which allows us to incorporate the adjacency condition about some entries in an occurrence of a generalized pattern. We use these trees to find functional equations for the generating functions enumerating these classes of permutations with respect to different parameters. In several cases we solve them using the kernel method and some ideas of Bousquet-Mélou [2]. We obtain refinements of known enumerative results and find new ones.

Permutations defining convex permutominoes

"Vegeu el resum a l'inici del document del fitxer adjunt."

On square permutations

Severini and Mansour introduced in [4]square polygons, as graphical representations of square permutations, that is, permutations such that all entries are records (left or right, minimum or maximum), and they obtained a nice formula for their number. In this paper we give a recursive construction for this class of permutations, that allows to simplify the derivation of their formula and to enumerate the subclass of square permutations with a simple record polygon. We also show that the generating function of these permutations with respect to the number of records of each type is algebraic, answering a question of Wilf in a particular case.

Clones de constantes et de permutations et leur intervalle monoïdal

Thèse diffusée initialement dans le cadre d'un projet pilote des Presses de l'Université de Montréal/Centre d'édition numérique UdeM (1997-2008) avec l'autorisation de l'auteur.

Inclusive Education, Person-Centered Planning & Systems Change Challenging Permutations and Opportunities

Resumen basado en el de la publicaci??n

Bit-index sort: a fast non-comparison integer sorting algorithm for permutations

This paper describes a fast integer sorting algorithm, herein referred as Bit-index sort, which is a non-comparison sorting algorithm for partial per-mutations, with linear complexity order in execution time. Bit-index sort uses a bit-array to classify input sequences of distinct integers, and exploits built-in bit functions in C compilers supported by machine hardware to retrieve the ordered output sequence. Results show that Bit-index sort outperforms in execution time to quicksort and counting sort algorithms. A parallel approach for Bit-index sort using two simultaneous threads is included, which obtains speedups up to 1.6.

BAliBASE (Benchmark Alignment dataBASE): enhancements for repeats, transmembrane sequences and circular permutations

BAliBASE is specifically designed to serve as an evaluation resource to address all the problems encountered when aligning complete sequences. The database contains high quality, manually constructed multiple sequence alignments together with detailed annotations. The alignments are all based on three-dimensional structural superpositions, with the exception of the transmembrane sequences. The first release provided sets of reference alignments dealing with the problems of high variability, unequal repartition and large N/C-terminal extensions and internal insertions. Here we describe version 2.0 of the database, which incorporates three new reference sets of alignments containing structural repeats, trans­membrane sequences and circular permutations to evaluate the accuracy of detection/prediction and alignment of these complex sequences. BAliBASE can be viewed at the web site http://www-igbmc.u-strasbg.fr/BioInfo/BAliBASE2/index.html or can be downloaded from ftp://ftp-igbmc.u-strasbg.fr/pub/BAliBASE2/.

Choice and chance, two chapters of arithmetic, with an appendix containing the algebraical treatment of permutations and combinations newly set forth.

Mode of access: Internet.

Extremal circular permutations with concave functions

Let {a(1), a(2), ..., a(n)} be a set of n distinct real numbers and let alpha(1), alpha(2), ..., alpha(n) an be a permutation of the numbers. We construct the permutation to maximise L-f = Sigma(i=1)(n) f(\alpha(i+1) - alpha(i)\), for any increasing concave function f, where we denote alpha(n+1) equivalent to alpha(1). The optimal permutation depends on the particular numbers {a(1), a(2), ..., a(n)} and the function f, contrary to a postulate by Chao and Liang (European J. Combin. 13 (1992) 325). (C) 2004 Elsevier Ltd. All rights reserved.

Dickson Polynomials that are Permutations

2000 Mathematics Subject Classification: 11T06, 13P10.

Bit-index sort: A fast non-comparison integer sorting algorithm for permutations

This paper describes a fast integer sorting algorithm, herein referred to as Bit-index sort, which does not use comparisons and is intended to sort partial permutations. Experimental results exhibit linear complexity order in execution time. Bit-index sort uses a bit-array to classify input sequences of distinct integers, and exploits built-in bit functions in C compilers, supported by machine hardware, to retrieve the ordered output sequence. Results show that Bit-index sort outperforms quicksort and counting sort algorithms when compared in their execution time. A parallel approach for Bit-index sort using two simultaneous threads is also included, which obtains further speedups of up to 1.6 compared to its sequential case.