We study q-analogues of k-Fibonacci numbers that arise from weighted tilings of an $n\times1$ board with tiles of length at most k. The weights on our tilings arise naturally out of distributions of permutations statistics and set partitions statistics. We use these q-analogues to produce q-analogues of identities involving k-Fibonacci numbers. This is a natural extension of results of the first author and Sagan on set partitions and the first author and Mathisen on permutations. In this paper we give general q-analogues of k-Fibonacci identities for arbitrary weights that depend only on lengths and locations of tiles. We then determine weights for specific permutation or set partition statistics and use these specific weights and the general identities to produce specific identities.
@article{10_37236_2550,
author = {Adam M Goyt and Brady L Keller and Jonathan E Rue},
title = {Statistical distributions and \(q\)-analogues of {\(k\)-Fibonacci} numbers},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2550},
zbl = {1267.05040},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2550/}
}
TY - JOUR
AU - Adam M Goyt
AU - Brady L Keller
AU - Jonathan E Rue
TI - Statistical distributions and \(q\)-analogues of \(k\)-Fibonacci numbers
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2550/
DO - 10.37236/2550
ID - 10_37236_2550
ER -
%0 Journal Article
%A Adam M Goyt
%A Brady L Keller
%A Jonathan E Rue
%T Statistical distributions and \(q\)-analogues of \(k\)-Fibonacci numbers
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/2550/
%R 10.37236/2550
%F 10_37236_2550
Adam M Goyt; Brady L Keller; Jonathan E Rue. Statistical distributions and \(q\)-analogues of \(k\)-Fibonacci numbers. The electronic journal of combinatorics, Tome 20 (2013) no. 1. doi: 10.37236/2550
