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A generalization of the symmetry between complete and elementary symmetric functions

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: M. Merca

Editorial: Indian Journal of Pure and Applied Mathematics, 45(1), p.75-89, 2014.

Rezumat:

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

URL: http://link.springer.com/article/10.1007/s13226-014-0052-0