In this paper we define the notion of singular composition of a positive integer. We provide a characterization of these compositions, together with methods for decomposing and also extending a singular composition in terms of other singular compositions. Consecutive extensions of particular compositions determine sequences of integers which coincide with classical integer sequences involving Fibonacci and Lucas numbers.

Aperiodic Compositions and Classical Integer Sequences

FERRARI, MARGHERITA MARIA;
2017-01-01

Abstract

In this paper we define the notion of singular composition of a positive integer. We provide a characterization of these compositions, together with methods for decomposing and also extending a singular composition in terms of other singular compositions. Consecutive extensions of particular compositions determine sequences of integers which coincide with classical integer sequences involving Fibonacci and Lucas numbers.
2017
ordered partition, composition, singular composition, Fibonacci number, Lucas number.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1033094
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