Autori: M. Merca
Editorial: Indian Journal of Pure and Applied Mathematics, 45(1), p.75-89, 2014.
A generalization for the symmetry between complete symmetric functions and elementary symmetric functions is given. As corollaries we derive the inverse of a triangular Toeplitz matrix and the expression of the Toeplitz-Hessenberg determinant. A very large variety of identities involving integer partitions and multinomial coefficients can be generated using this generalization. The partitioned binomial theorem and a new formula for the partition function p(n) are obtained in this way.
Cuvinte cheie: Complete symmetric functions, elementary symmetric functions, multinomial coefficients, integer partitions