IJPAM: Volume 65, No. 4 (2010)

PERMUTATIONS WITH RISES AS CHARACTERISTICS OF
CYCLES FORMED BY GENERALIZED GOLDEN RATIOS:
A SEMI-EXPERIMENTAL APPROACH

Sergei Abramovich$^1$, Gennady A. Leonov$^2$
$^1$School of Education and Professional Studies
State University of New York
44 Pierrepont Ave, Potsdam, NY 13676-2294, USA
e-mail: abramovs@potsdam.edu
$^2$Faculty of Mathematics and Mechanics
St. Petersburg State University
Universitetskyi, 28, Peterhof, St.Petersburg, 198504, RUSSIA
e-mail: leonov@math.spbu.ru


Abstract.The article studies the behavior of cycles formed by the orbits of a two-parametric linear difference equation of the second order, a generalization of the Fibonacci recursion. Permutations with rises are suggested as universal characteristics of the cycles across the whole spectrum of integer periods. The method used by the authors is a combination of Maple-based computational experiments and formal demonstration.

Received: October 20, 2010

AMS Subject Classification: 12-04, 11C08

Key Words and Phrases: Fibonacci-like polynomials, generalized golden ratios, cycles, permutations with rises, Maple

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 65
Issue: 4