Comments on Combinatorial Interpretation

Abstract

To our knowledge - for about 126 years we have lacked a classical type combinatorial interpretation of Fibonomial coefficients. Lukas [1] - to our knowledge - was the first who defined Fibonomial coefficients and derived a recurrence for them (see Historical Note in [2]). As noted by Knuth and Wilf in [3], the recurrence relations for Fibonomial coefficients appeared already in 1878. Lukas's work [1] Theorie des Fonctions Numeriques Simplement Periodiques is the proper context for binomial and binomial-type coefficients - Fibonomial coefficients included.