Counting 1324-Avoiding Permutations

We consider permutations that avoid the pattern 1324. By studying the generating tree for such permutations, we obtain a recurrence formula for their number. A computer program provides data for the number of 1324-avoiding permutations of length up to 20.

[1]  Ira M. Gessel,et al.  Symmetric functions and P-recursiveness , 1990, J. Comb. Theory, Ser. A.

[2]  Neil J. A. Sloane,et al.  The encyclopedia of integer sequences , 1995 .

[3]  Miklós Bóna Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps , 1997, J. Comb. Theory, Ser. A.

[4]  Zvezdelina Stankova,et al.  Forbidden subsequences , 1994, Discret. Math..

[5]  Zvezdelina Stankova Classification of Forbidden Subsequences of Length 4 , 1996, Eur. J. Comb..

[6]  Julian West,et al.  Generating trees and forbidden subsequences , 1996, Discret. Math..

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

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

[9]  Amitai Regev,et al.  Asymptotic values for degrees associated with strips of young diagrams , 1981 .

[10]  Julian West,et al.  Generating trees and the Catalan and Schröder numbers , 1995, Discret. Math..

[11]  R. Bellman Dynamic programming. , 1957, Science.

[12]  Rodica Simion,et al.  Restricted Permutations , 1985, Eur. J. Comb..

[13]  Donald E. Knuth,et al.  The art of computer programming: sorting and searching (volume 3) , 1973 .

[14]  D. Michie “Memo” Functions and Machine Learning , 1968, Nature.

[15]  Fan Chung Graham,et al.  The Number of Baxter Permutations , 1978, J. Comb. Theory, Ser. A.

[16]  Herbert S. Wilf,et al.  The patterns of permutations , 2002, Discret. Math..

[17]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[18]  Miklós Bóna,et al.  Permutations avoiding certain patterns: The case of length 4 and some generalizations , 1997, Discret. Math..