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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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2023-03-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/341 |
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| Summary: | 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 $\{ B_{m,n}(x,y) \}$. |
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| ISSN: | 1027-4634 2411-0620 |