Self-describing sequences and the Catalan family tree

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We introduce a transformation of finite integer sequences, show that every sequence eventually stabilizes under this transformation and that the number of fixed points is counted by the Catalan numbers. The sequences that are fixed are precisely those that describe themselves -- every term $t$ is equal to the number of previous terms that are smaller than $t$. In addition, we provide an easy way to enumerate all these self-describing sequences by organizing them in a Catalan tree with a specific labelling system.
9 pages, 2 figures. submitted to Electronic Journal of Combinatorics

Keywords

Combinatorics, 05A15; 05C05; 11Y55

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/67537

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0305319
 http://arxiv.org/abs/math/0305319

Collections

arXiv