Topic
Catalan's triangle
About: Catalan's triangle is a research topic. Over the lifetime, 4 publications have been published within this topic receiving 41 citations.
Papers
TL;DR: This paper studies eight mesh patterns of small lengths and links avoidance of one of the patterns to the harmonic numbers, while for three other patterns it is shown their distributions on 132-avoiding permutations are given by the Catalan triangle.
26 citations
TL;DR: In this paper, an identity relating Fibonacci numbers to Pascal's triangle discovered by G.E. Andrews is presented, based on a Riordan array argument, and the main point of the proof is the construction of a new Riordan arrays from a given Riordanarray, by the elimination of elements.
16 citations
Posted Content•
TL;DR: In this paper, the authors study eight mesh patterns of small lengths and link avoidance of one of the patterns to the harmonic numbers, while for three other patterns they show their distributions on 132-avoiding permutations are given by the Catalan triangle.
Abstract: The notion of a mesh pattern was introduced recently, but it has already proved to be a useful tool for description purposes related to sets of permutations. In this paper we study eight mesh patterns of small lengths. In particular, we link avoidance of one of the patterns to the harmonic numbers, while for three other patterns we show their distributions on 132-avoiding permutations are given by the Catalan triangle. Also, we show that two specific mesh patterns are Wilf-equivalent. As a byproduct of our studies, we define a new set of sequences counted by the Catalan numbers and provide a relation on the Catalan triangle that seems to be new.
15 citations
5 Dec 2016
TL;DR: This work investigates the enumeration of non-crossing tree realizations of integer sequences, and considers a special case in four parameters, that can be seen as a four-dimensional tetrahedron that generalizes Pascal's triangle and the Catalan numbers.
Abstract: We investigate the enumeration of non-crossing tree realizations of integer sequences, and we consider a special case in four parameters, that can be seen as a four-dimensional tetrahedron that generalizes Pascal's triangle and the Catalan numbers. This work is motivated by the study of ambiguities in categorial grammars.
2 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 2013 | 1 |
| 2012 | 1 |
| 2008 | 1 |