Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials
This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\inf...
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| Format: | Article |
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Ivan Franko National University of Lviv
2025-06-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/610 |
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| author | V. V. Kravtsiv P. Y. Dolishniak R. Y. Stakhiv |
| author_facet | V. V. Kravtsiv P. Y. Dolishniak R. Y. Stakhiv |
| author_sort | V. V. Kravtsiv |
| collection | DOAJ |
| description | This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\infty$ and spaces of two-sided absolutely summing series of vectors in $\mathbb{C}^s$ for some positive integer $s>1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications. |
| format | Article |
| id | doaj-art-0038e06ae70c4f0dbe51f4fea8b5a1fb |
| institution | DOAJ |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2025-06-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-0038e06ae70c4f0dbe51f4fea8b5a1fb2025-08-20T03:17:40ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202025-06-0163221022010.30970/ms.63.2.210-220610Waring-Girard formulas for block-symmetric and block-supersymmetric polynomialsV. V. Kravtsiv0P. Y. Dolishniak1R. Y. Stakhiv2Vasyl Stefanyk Carpathian National University, Ivano-Frankivsk, UkraineVasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, UkraineVasyl Stephanyk Precarpathian National University, Ivano-Frankivsk, UkraineThis paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\infty$ and spaces of two-sided absolutely summing series of vectors in $\mathbb{C}^s$ for some positive integer $s>1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications.http://matstud.org.ua/ojs/index.php/matstud/article/view/610block-symmetric polynomialblock-supersymmetric polynomialwaring-girard formulaalgebraic basescombinatorial relation |
| spellingShingle | V. V. Kravtsiv P. Y. Dolishniak R. Y. Stakhiv Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials Математичні Студії block-symmetric polynomial block-supersymmetric polynomial waring-girard formula algebraic bases combinatorial relation |
| title | Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials |
| title_full | Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials |
| title_fullStr | Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials |
| title_full_unstemmed | Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials |
| title_short | Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials |
| title_sort | waring girard formulas for block symmetric and block supersymmetric polynomials |
| topic | block-symmetric polynomial block-supersymmetric polynomial waring-girard formula algebraic bases combinatorial relation |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/610 |
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