Mixed succession rules: the commutative case

Details Mixed succession rules: the commutative case Mixed succession rules: the commutative case

2008-06-04

arxiv.org/abs/0806.0799v1

Mathematics

Combinatorics

28 pages, submitted

Scientific paper

We begin a systematic study of the enumerative combinatorics of mixed succession rules, which are succession rules such that, in the associated generating tree, the nodes are allowed to produce their sons at several different levels according to different production rules. Here we deal with a specific case, namely that of two different production rules whose rule operators commute. In this situation, we are able to give a general formula expressing the sequence associated with the mixed succession rules in terms of the sequences associated with the component production rules. We end by providing some examples illustrating our approach.

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