Complex Systems

Permutation Numbers Download PDF

Vincenzo De Florio
Department of Electrical Engineering, University of Leuven,
Kasteelpark Arenberg 10, 3001 Leuven-Heverlee, Belgium


This paper investigates some series of integers which are derived from a recursively defined sequence of permutations of words. Such a recursion can be interpreted as a dynamic system. Geometrical representations of these series appear to be self-similar, symmetrical, and factorizable. The paper also shows how some bidimensional images may be decomposed into images corresponding to permutations of fewer symbols.