Sign balances and promotion order of Young-Fibonacci tableaux

Abstract

In this paper we give two results on Young Fibonacci tableaux. First we establish identities about the sign balances of Young Fibonacci tableaux, analog to known results on standard Young tableaux. Then we investigate the promotion action on a Young Fibonacci tableau and determine the order of the action. In contrast with the fact that there is no general formula of the promotion order for a standard Young tableau, here we can determine the order completely.