A note on mobiusien function and mobiusien inversion formula of fibonacci cobweb poset

The Fibonacci cobweb poset P has been introduced by A.K.Kwaśniewski in [3, 4] for the purpose of finding combinatorial interpretation of fibonomial coefficients and their reccurence relation. At first the partially ordered set P (Fibonacci cobweb poset) was defined via its Hasse diagram as follows: It looks like famous rabbits grown tree but it has the specific cobweb in addition, i.e. it consists of levels labeled by Fibonacci numbers (the n-th level consist of Fn elements). Every element of n-th level (n ≥ 1, n ∈ N) is in partial order relation with every element of the (n + 1)-th level but it’s not with any element from the level in which he lies (n-th level) except from it.