Article
Licensed
Unlicensed
Requires Authentication
Combinatorial Interpretations of Convolutions of the Catalan Numbers
-
Steven J. Tedford
Published/Copyright:
February 24, 2011
Abstract
We reintroduce an interpretation of the kth-fold self convolution of the Catalan numbers by showing that they count the number of words in symbols X and Y, where the total number of Y's is k more than the total number of X's, and at no time are there more Y's than k plus the number of X's. Using this, we exhibit some of the wide variety of combinatorial interpretations of the kth-fold self convolution of the Catalan numbers. Finally, we show how these numbers appear as the last column in a truncated Pascal's triangle.
Received: 2010-05-23
Revised: 2010-08-18
Accepted: 2010-09-27
Published Online: 2011-02-24
Published in Print: 2011-February
© de Gruyter 2011
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
Articles in the same Issue
- Symmetries in Steinhaus Triangles and in Generalized Pascal Triangles
- Unbounded Discrepancy in Frobenius Numbers
- Combinatorial Interpretations of Convolutions of the Catalan Numbers
- Quadratic Forms and Four Partition Functions Modulo 3
- On Bases with a T-Order
- Van der Waerden's Theorem and Avoidability in Words
- On a Class of Ternary Inclusion-Exclusion Polynomials
