Combinatorial Proofs Of Three Identities

Using the Lagrange inversion formula,Y.Sun obtained the following two binomial coefficient identities: We give a q-analogue of Sun's identities as follows: We provide two proofs,one of which is combinatorial via partitions.Munarini[22]obtained the following identity by Cauchy's integral formula: Guo[14]gave a multinomial coefficient generalization of Munarini's identity as fol0 lows: where n=(n1,…,nm),｜n｜=n1+…+nm,(nx)=x(x-1)…(x-｜n｜+1)/n1!…nm!,and xk= x1k1…xmkm.The second aim of this paper is to present a combinatorial proof of Guo's identity.