Fwd: [E-JC] From the Electronic Journal of Combinatorics

[Olivier Gerard]

This freely available preprints may be of interest to
members of seqfan.

Olivier


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From: E-JC <eljc at math.upenn.edu>

The following note has been published in
The Electronic Journal of Combinatorics.  

It can be viewed at <http://www.combinatorics.org>.
Click on the button or link for Volume 10 (1).

==============================

N5. Zoran Sunik: 

       Self-Describing Sequences and the Catalan Family Tree      


Abstract:

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.

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