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A generalization of the symmetry between complete and elementary symmetric functions

Author

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  • Mircea Merca

    (University of Craiova)

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.

Suggested Citation

  • Mircea Merca, 2014. "A generalization of the symmetry between complete and elementary symmetric functions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(1), pages 75-90, February.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:1:d:10.1007_s13226-014-0052-0
    DOI: 10.1007/s13226-014-0052-0
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    Cited by:

    1. Ali Boussayoud & Salah Boulaaras & Ali Allahem, 2024. "Novel Classes on Generating Functions of the Products of (p,q)-Modified Pell Numbers with Several Bivariate Polynomials," Mathematics, MDPI, vol. 12(18), pages 1-24, September.

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