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EnglishWe want to illustrate some correspondences between Catalan numbers and combinatoric objects, such as plane walks, binary trees and some particular words. By means of under-diagonal walks, we give a combinatorial interpretation of the formula Cn = 1 n+1 2n n defining Catalan numbers. These numbers also enumerate both words in a particular language defined on a four character alphabet and the corresponding walks made up of four different types of steps. We illustrate a bijection between n-long words in this language and binary trees having n + 1 nodes, after which we give a simple proof of Touchard's formula.
Some more properties of Catalan numbers / E. BARCUCCI; M. C. VERRI. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - STAMPA. - 102(1992), pp. 229-237.
| Titolo: | Some more properties of Catalan numbers | |
| Autori di Ateneo: | ||
| Autori: | BARCUCCI, ELENA; VERRI, MARIA CECILIA | |
| Anno di registrazione: | 1992 | |
| Rivista: | ||
| Volume: | 102 | |
| Pagina iniziale: | 229 | |
| Pagina finale: | 237 | |
| Abstract: | We want to illustrate some correspondences between Catalan numbers and combinatoric objects, such as plane walks, binary trees and some particular words. By means of under-diagonal walks, we give a combinatorial interpretation of the formula Cn = 1 n+1 2n n defining Catalan numbers. These numbers also enumerate both words in a particular language defined on a four character alphabet and the corresponding walks made up of four different types of steps. We illustrate a bijection between n-long words in this language and binary trees having n + 1 nodes, after which we give a simple proof of Touchard's formula. | |
| Handle: | http://hdl.handle.net/2158/10704 | |
| Appare nelle tipologie: | 1a - Articolo su rivista |
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