A generalization of the symmetry between complete and elementary symmetric functions

Mircea Merca ()
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Mircea Merca: University of Craiova

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 1, 75-90

Abstract: 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.

Keywords: Complete symmetric functions; elementary symmetric functions; multinomial coefficients; integer partitions (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s13226-014-0052-0

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