Goulden and Jackson introduced the cluster method for counting words avoiding a prescribed set of subwords in [14, 15]. Noonan and Zeilberger  generalized it and wrote many Maple programs to implement the method and its extensions. We count Dyck paths according to the number of occurrences of certain patterns, using a variation of the Goulden-Jackson cluster method. We will give several examples of counting Dyck paths by occurrences of subwords and show how to use the cluster method to compute generating functions for those examples. Then we show more applications to count paths with bounded height by occurrences of subwords and more applications to count r–Dyck paths.
|Commitee:||Li, Ji, Parker, Susan|
|School Location:||United States -- Massachusetts|
|Source:||DAI-B 72/12, Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Mathematics|
|Keywords:||Cluster method, Combinatorics, Dyck path, Goulden-Jackson cluster, Occurrences of subwords|
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