Counting occurrences of some subword patterns

We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the number of strings containing a specified number of occurrences of a given 3-letter subword pattern.

[1]  Mireille Régnier,et al.  On the approximate pattern occurrences in a text , 1997, Proceedings. Compression and Complexity of SEQUENCES 1997 (Cat. No.97TB100171).

[2]  Mike D. Atkinson,et al.  Restricted permutations , 1999, Discret. Math..

[3]  David Thomas,et al.  The Art in Computer Programming , 2001 .

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

[5]  T. Mansour,et al.  Words Restricted by 3-Letter Generalized Multipermutation Patterns , 2001, math/0112281.

[6]  Eric Babson,et al.  Generalized permutation patterns and a classification of the Mahonian statistics , 2000 .

[7]  Toufik Mansour,et al.  Counting Occurrences of 132 in a Permutation , 2002, Adv. Appl. Math..

[8]  A. Burstein.  Enumeration of words with forbidden patterns , 1998 .

[9]  Miklós Bóna.  Permutations with one or two 132-subsequences , 1998, Discret. Math..

[10]  D. Zeilberger,et al.  The Enumeration of Permutations with a Prescribed Number of “Forbidden” Patterns , 1996, math/9808080.

[11]  Toufik Mansour,et al.  Words Restricted by Patterns with at Most 2 Distinct Letters , 2001, Electron. J. Comb..

[12]  H. Davenport,et al.  A Combinatorial Problem Connected with Differential Equations , 1965 .

[14]  I. Goulden,et al.  Combinatorial Enumeration , 2004 .

[15]  M. Bóna,et al.  The Number of Permutations with Exactlyr132-Subsequences IsP-Recursive in the Size! , 1997 .

[16]  John Noonan.  The number of permutations containing exactly one increasing subsequence of length three , 1996, Discret. Math..

[17]  A. Odlyzko.  Asymptotic enumeration methods , 1996 .