Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903664 | European Journal of Combinatorics | 2017 | 22 Pages |
Abstract
The Catalan number Cn enumerates parenthesizations of x0ââ¯âxn where â is a binary operation. We introduce the modular Catalan number Ck,n to count equivalence classes of parenthesizations of x0ââ¯âxn when â satisfies a k-associative law generalizing the usual associativity. This leads to a study of restricted families of Catalan objects enumerated by Ck,n with emphasis on binary trees, plane trees, and Dyck paths, each avoiding certain patterns. We give closed formulas for Ck,n with two different proofs. For each nâ¥0 we compute the largest size of k-associative equivalence classes and show that the number of classes with this size is a Catalan number.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Nickolas Hein, Jia Huang,