Analogues of Waring-Girard formulas for the block-symmetric polynomials on the spaces  $\ell_1(\mathbb{c}^2)$ and $\ell_p(\mathbb{c}^2)$

Viktoriia Kravtsiv, Mariia Martsinkiv, Andrii Yaselskyi

Анотація


Classical Waring-Girard formulas gives a representation of elementary  and complete symmetric polynomials though the power symmetric polynomials. In this paper, we propose an analog of the Waring-Girard formulas for block-symmetric polynomials on the   spaces $\ell_1(\mathbb{C}^2)$ and $\ell_p(\mathbb{C}^2)$ and show the application of the obtained formula in combinatorics.

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H. Weyl, The classical group: their invariants and representations, Princeton university press: Princenton, New Jersey, 1973.

A. Nemirovskii and S. Semenov, On polynomial approximation of functions on Hilbert space, Mat. USSR-Sb. 21 (1973), 255-277. DOI: 10.1070/SM1973v021n02ABEH002016

M. Gonzacutealez, R. Gonzalo, and J. A. Jaramillo, Symmetric polynomials on rearrangement-invariant function spaces, J. Lond. Math. Soc. 59 (1999), no. 2, 681--697. DOI: 10.1112/S0024610799007164

M. Rosas, MacMahon symmetric functions, the partition lattice, and Young subgroups, J. Combin. Theory Ser. A 96 (2001), no. 2, 326--340. DOI: 10.1006/jcta.2001.3186

V. Kravtsiv, T. Vasylyshyn, and A. Zagorodnyuk, On algebraic basis of the algebra of symmetric polynomials on $ell_p(mathbb{C}^n)$, J. Funct. Spaces. 2017 (2017), Article ID 4947925, 8 pages. DOI: 10.1155/2017/4947925

A. Bandura, V. Kravtsiv, and T. Vasylyshyn, Algebraic basis of the algebra of all symmetric continuous polynomials on the cartesian product of $ell_p$-spaces. Axioms. 11 (2022), no. 2, Article 41. DOI: 10.3390/axioms11020041

V. V. Kravtsiv, Analogues of the Newton formulas for the block-symmetric polynomials, Carpathian Math. Publ. 12 (2020), no. 1, 17-22. DOI: 10.15330/cmp.12.1.17-22

V. Kravtsiv, The analogue of Newton’s formula for block-symmetric polynomials,
International Journal of Mathematical Analysis 10 (2016), no. 7, 323-327. DOI: 10.12988/ijma.2016.617

P. A. MacMahon, Combynatory analysis, Vol. I. University Press, Cambridge, 1915.

O. V. Handera-Kalynovska and V. V. Kravtsiv, The Waring-Girard formulas for symmetric polynomials on spaces $ell_p$, Carpathian Math. Pabl. 16 (2024), no. 2, 407--413. DOI: 0.15330/cmp.16.2.407-413

А. В. Загороднюк, В. В. Кравців, Мультиплікативна згортка на алгебрі блочно-си-метричних аналітичних функцій, Мат. методи фіз.-мех. поля 60 (2017), no. 3, 107--114; English version: A. V. Zagorodnyuk and V. V. Kravtsiv, Multiplicative convolution on the algebra of block-semmetric analytic functions, J. Math. Sci. 246 (2020), no. 2, 245--255. DOI: 10.1007/s10958-020-04734-z

V. V. Kravtsiv and A. Zagorodnyuk, Spectra of algebras of block-symmetric analytic functions of bounded type, Mat. Stud. 58 (2022), no. 1, 69–81. DOI: 10.30970/ms.58.1.69-81

V. Kravtsiv, Block-supersymmetric polynomials on spaces of absolutely convergent series, Symmetry. 16 (2024), no. 2, Article 197. DOI: 10.3390/sym16020179




DOI: http://dx.doi.org/10.30970/vmm.2024.96.061-070

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