Journal of Integer Sequences, Vol. 10 (2007), Article 07.8.8

Generalizations of Carlitz Compositions


Sylvie Corteel
LRI
CNRS Université Paris-Sud
91405 Orsay
France

Paweł Hitczenko
LRI
CNRS Université Paris-Sud
91405 Orsay
France
and
Department of Mathematics
Drexel University
Philadelphia, PA 19104
USA

Abstract:

We consider a class of generating functions that appear in the context of Carlitz compositions. In order to combinatorially interpret them, we introduce a combinatorial structures that we name generalized compositions and p-Carlitz compositions of integers. We explain their connection to Carlitz compositions, the relation to other combinatorial structures, and we describe their basic properties.

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(Concerned with sequences A003242 A129921 and A129922 .)

Received June 6 2007; revised versions received August 3 2007; August 19 2007. Published in Journal of Integer Sequences, August 19 2007.

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