Generating involutions, derangements, and relatives by ECO

We show how the ECO method can be applied to exhaustively generate some classes of permutations. A previous work initiating this technique and motivating our research was published in Ac ta Informatica, 2004, by S. Bacchelli, E. Barcucci, E. Grazzini and E. Pergola.

[1]  Philippe Flajolet,et al.  Non-overlapping Partitions, Continued Fractions, Bessel Functions and a Divergent Series , 1990, Eur. J. Comb..

[2]  Anders Claesson,et al.  Generalized Pattern Avoidance , 2001, Eur. J. Comb..

[3]  Jean-Luc Baril.  More restrictive Gray codes for some classes of pattern avoiding permutations , 2009, Inf. Process. Lett..

[4]  Antonio Bernini,et al.  A general exhaustive generation algorithm for Gray structures , 2007, Acta Informatica.

[5]  Renzo Pinzani,et al.  Jumping succession rules and their generating functions , 2003, Discret. Math..

[6]  Toufik Mansour,et al.  Combinatorial Gray codes for classes of pattern avoiding permutations , 2008, Theor. Comput. Sci..

[7]  T. Walsh.  Gray Codes for Involutions , 2010 .

[8]  Vincent Vajnovszki,et al.  Generating restricted classes of involutions, Bell and Stirling permutations , 2010, Eur. J. Comb..

[9]  Jean-Luc Baril,et al.  Gray code for derangements , 2004, Discret. Appl. Math..

[10]  Elena Barcucci,et al.  Exhaustive generation of combinatorial objects by ECO , 2004, Acta Informatica.

[11]  Selmer M. Johnson.  Generation of permutations by adjacent transposition , 1963 .

[12]  Jean-Luc Baril,et al.  ECO-Generation for p-generalized Fibonacci and Lucas permutations , 2006 .

[13]  Gideon Ehrlich,et al.  Loopless Algorithms for Generating Permutations, Combinations, and Other Combinatorial Configurations , 1973, JACM.

[14]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

[15]  Alberto Del Lungo,et al.  ECO:a methodology for the enumeration of combinatorial objects , 1999 .

[16]  Robert Sedgewick,et al.  Permutation Generation Methods , 1977, CSUR.

[17]  R. Stanley.  What Is Enumerative Combinatorics , 1986 .

[18]  D. H. Lehmer.  Permutation by Adjacent Interchanges , 1965 .

[19]  Jean-Luc Baril,et al.  Gray code for permutations with a fixed number of cycles , 2007, Discret. Math..

[20]  Gilbert Labelle,et al.  Stirling numbers interpolation using permutations with forbidden subsequences , 2002, Discret. Math..