Abstract
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.
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Merca, M. A generalization of the symmetry between complete and elementary symmetric functions. Indian J Pure Appl Math 45, 75–90 (2014). https://doi.org/10.1007/s13226-014-0052-0
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DOI: https://doi.org/10.1007/s13226-014-0052-0