Aperiodic Compositions and Classical Integer Sequences.
Aperiodic Compositions and Classical Integer Sequences.
Summary: 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.
singular composition, Combinatorial aspects of partitions of integers, ordered partition, composition, Lucas number, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci number, ordered partition, composition, singular composition, Fibonacci number, Lucas number.
singular composition, Combinatorial aspects of partitions of integers, ordered partition, composition, Lucas number, Fibonacci and Lucas numbers and polynomials and generalizations, Fibonacci number, ordered partition, composition, singular composition, Fibonacci number, Lucas number.
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