Pseudo-involutions in the Riordan group and Chebyshev polynomials
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916620583043072 |
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| author | Burstein, Alexander Shapiro, Louis W. |
| author_facet | Burstein, Alexander Shapiro, Louis W. |
| contents | Generalizing the results in our previous paper, we consider pseudo-involutions in the Riordan group where the generating function $g$ for the first column of a Riordan array satisfies a functional equation of certain types involving a polynomial. For those types of equations, we find the pseudo-involutory companion of $g$. We also develop a general method for finding B-functions of Riordan pseudo-involutions in the cases we consider, and show that these B-functions involve Chebyshev polynomials. We apply our method for several families of Riordan arrays, obtaining new results and deriving known results more efficiently. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13673 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pseudo-involutions in the Riordan group and Chebyshev polynomials Burstein, Alexander Shapiro, Louis W. Combinatorics 05A15 (Primary) 05A05, 05A19, 11B83 (Secondary) Generalizing the results in our previous paper, we consider pseudo-involutions in the Riordan group where the generating function $g$ for the first column of a Riordan array satisfies a functional equation of certain types involving a polynomial. For those types of equations, we find the pseudo-involutory companion of $g$. We also develop a general method for finding B-functions of Riordan pseudo-involutions in the cases we consider, and show that these B-functions involve Chebyshev polynomials. We apply our method for several families of Riordan arrays, obtaining new results and deriving known results more efficiently. |
| title | Pseudo-involutions in the Riordan group and Chebyshev polynomials |
| topic | Combinatorics 05A15 (Primary) 05A05, 05A19, 11B83 (Secondary) |
| url | https://arxiv.org/abs/2502.13673 |