  The Fibonomial and Gaussian binomial coefficients are well known analogues of
the binomial coefficients. A combinatorial interpretation for these analogues
was first presented by Sagan and Savage in 2010. We introduce a slightly
modified interpretation of Fibonomial coefficients. We also prove some
identities involving Gaussian binomial coefficients. Recently Bergeron gave a
similar interpretation of the q Fibonomial coefficients. Inspired from the
model given by Bennett, they obtained a staircase model for the q Fibonomial
coefficients as well. They have provided the proofs for the same using
induction and bijective correspondence techniques. We establish a new model for
q Fibonacci numbers using which we can give a non bijective proof to the
staircase model. We apply this model to prove some identities of q Fibonacci
numbers. Also we will demonstrate some identities related to the q Fibonomial
coefficients using the staircase model.
