AN IDENTITY ON SYMMETRIC POLYNOMIALS
DOI:
https://doi.org/10.37569/DalatUniversity.10.2.684(2020)Keywords:
Interpolation theory, Lagrange interpolation formula, Symmetric polynomials.Abstract
In this paper, we propose and prove an identity on symmetric polynomials. In order to obtain this identity, we use the interpolation theory, in particular, the Lagrange interpolation formula. In the proof of the identity, we propose two different proofs. The second proof will be the first step for our further studies related to identities on symmetric polynomials.
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References
Chen, W. Y. C. & Louck, J. D. (1996). Interpolation for symmetric functions. Advances in Mathematics, 117, 147-156.
Cox, D. A., Little, J., & O’Shea, D. (2007). Ideals, varieties, and algorithms: An introduction to computational algebraic geometry and commutative algebra (3rd edition). New York, USA: Springer Publishing.
Dang, T. H. (2019). Identities involving (doubly) symmetric polynomials and integrals over Grassmannians. Fundamenta Mathematicae, 246(2), 181-191.
Zeilberger, D. (1982). A combinatorial proof of Dyson’s conjecture. Discrete Mathematics, 41(3), 317-321.
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Copyright (c) 2020 Đặng Tuấn Hiệp, Lê Văn Vĩnh.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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