An algebraic characterization of the set of succession rules

Authors:
Luca Ferrari;Elisa Pergola;Renzo Pinzani;Simone Rinaldi
Affiliations:
U. Dini, Firenze, Italy;Dipartimento di Sistemi e Informatica, Firenze, Italy;Dipartimento di Sistemi e Informatica, Firenze, Italy;Dipartimento di Sistemi e Informatica, Firenze, Italy
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

In this paper we will give a formal description of succession rules in terms of linear operators satisfying certain conditions. This representation allows us to introduce a system of well-defined operations into the set of succession rules and then to tackle problems of combinatorial enumeration simply by using operators instead of generating functions. Finally, we will suggest several open problems whose solution should lead to an algebraic characterization of the set of succession rules.