Two Approaches to Normal Order Coefficients

摘要

We consider the normal ordering coefficients of strings consisting of the symbols V, U which satisfy the commutation rule UV - qVU = hVs. These coefficients are studied using two approaches. First, we continue the study by Varvak, where the coefficients were interpreted as q-rook numbers under the row creation rook model introduced by Goldman and Haglund. Second, we express the coefficients in terms of a kind of generalization of some symmetric functions. We derive identities involving the coefficients including some explicit formulas.