Bi-periodic Fibonomial Coefficients

Abstract

In the present study, we introduce a new generalization of Fibonomial coefficients known
as bi-periodic Fibonomial coefficients, which can be expressed in relation to bi-periodic Fibonacci numbers. We establish various properties of these coefficients, including recurrence relation and recurrence formulas for powers of the bi-periodic Fibonacci numbers. Moreover, we provide combinatorial interpretation through weighted tilings generated by lattice paths and offer combinatorial proofs for bi-periodic Fibonomial identities.