Nowy tom czasopisma Symmetry przynosi artykuł autorstwa D. Strzałka, A. Włoch i S. Wolski. W artykule wprowadzone zostały nowe uogólnienia, w sensie odległości, wielomianów Fibonacciego. Badane są własności tych wielomianów będących uogólnieniem między innymi liczb Fibonacciego, Jacobsthala, Narayana.
Strzałka, D.; Wolski, S.; Włoch, A. Distance Fibonacci Polynomials by Graph Methods. Symmetry 2021, 13, 2075. https://doi.org/10.3390/sym13112075
Abstract
In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions
