Quasi-monomials with respect to subgroups of the plane affine group
Let $H$ be a subgroup of the plane affine group ${\rm Aff}(2)$ considered with the natural action on the vector space of two-variable polynomials. The polynomial family $\{ B_{m,n}(x,y) \}$ is called quasi-monomial with respect to $H$ if the group operators in two different bases $ \{ x^m y^n \} $ a...
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Ivan Franko National University of Lviv
2023-03-01
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| Series: | Математичні Студії |
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| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/341 |
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| author | N. M. Samaruk |
| author_facet | N. M. Samaruk |
| author_sort | N. M. Samaruk |
| collection | DOAJ |
| description | Let $H$ be a subgroup of the plane affine group ${\rm Aff}(2)$ considered with the natural action on the vector space of two-variable polynomials. The polynomial family $\{ B_{m,n}(x,y) \}$ is called quasi-monomial with respect to $H$ if the group operators in two different bases $ \{ x^m y^n \} $ and $\{ B_{m,n}(x,y) \}$ have \textit{identical} matrices. We obtain a criterion of quasi-monomiality for the case when the group $H$ is generated by rotations and translations in terms of exponential generating function for the polynomial family $\{ B_{m,n}(x,y) \}$. |
| format | Article |
| id | doaj-art-a170cf938d0341c0af8cc229a28cb3f2 |
| institution | Kabale University |
| issn | 1027-4634 2411-0620 |
| language | deu |
| publishDate | 2023-03-01 |
| publisher | Ivan Franko National University of Lviv |
| record_format | Article |
| series | Математичні Студії |
| spelling | doaj-art-a170cf938d0341c0af8cc229a28cb3f22025-08-20T03:28:41ZdeuIvan Franko National University of LvivМатематичні Студії1027-46342411-06202023-03-0159131110.30970/ms.59.1.3-11341Quasi-monomials with respect to subgroups of the plane affine groupN. M. Samaruk0Vasyl Stefanyk Precarpathian National UniversityLet $H$ be a subgroup of the plane affine group ${\rm Aff}(2)$ considered with the natural action on the vector space of two-variable polynomials. The polynomial family $\{ B_{m,n}(x,y) \}$ is called quasi-monomial with respect to $H$ if the group operators in two different bases $ \{ x^m y^n \} $ and $\{ B_{m,n}(x,y) \}$ have \textit{identical} matrices. We obtain a criterion of quasi-monomiality for the case when the group $H$ is generated by rotations and translations in terms of exponential generating function for the polynomial family $\{ B_{m,n}(x,y) \}$.http://matstud.org.ua/ojs/index.php/matstud/article/view/341group action; quasi-monomials; generating functions; plane affine group; pattern recognition |
| spellingShingle | N. M. Samaruk Quasi-monomials with respect to subgroups of the plane affine group Математичні Студії group action; quasi-monomials; generating functions; plane affine group; pattern recognition |
| title | Quasi-monomials with respect to subgroups of the plane affine group |
| title_full | Quasi-monomials with respect to subgroups of the plane affine group |
| title_fullStr | Quasi-monomials with respect to subgroups of the plane affine group |
| title_full_unstemmed | Quasi-monomials with respect to subgroups of the plane affine group |
| title_short | Quasi-monomials with respect to subgroups of the plane affine group |
| title_sort | quasi monomials with respect to subgroups of the plane affine group |
| topic | group action; quasi-monomials; generating functions; plane affine group; pattern recognition |
| url | http://matstud.org.ua/ojs/index.php/matstud/article/view/341 |
| work_keys_str_mv | AT nmsamaruk quasimonomialswithrespecttosubgroupsoftheplaneaffinegroup |