Mixed succession rules: The commutative case

Authors:
Silvia Bacchelli;Luca Ferrari;Renzo Pinzani;Renzo Sprugnoli
Affiliations:
Liceo Scientifico Statale “Copernico”, via Garavaglia 11, 40127 Bologna, Italy;Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy;Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy;Dipartimento di Sistemi e Informatica, viale Morgagni 65, 50134 Firenze, Italy
Venue:
Journal of Combinatorial Theory Series A
Year:
2010

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Abstract

We begin a systematic study of the enumerative combinatorics of mixed succession rules, i.e. succession rules such that, in the associated generating tree, nodes are allowed to produce 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 rule in terms of the sequences associated with the component production rules. We end by providing examples illustrating our approach.