Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916659154911232 |
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| author | Liu, Feihu Wang, Ying Zhang, Yingrui Zhang, Zihao |
| author_facet | Liu, Feihu Wang, Ying Zhang, Yingrui Zhang, Zihao |
| contents | Cigler considered certain shifted Hankel determinants of convolution powers of Catalan numbers and conjectured identities for these determinants. Recently, Fulmek gave a bijective proof of Cigler's conjecture. Cigler then provided a computational proof. We extend Cigler's determinant identities to the convolution of general power series $F(x)$, where $F(x)$ satisfies a certain type of quadratic equation. As an application, we present the Hankel determinant identities of convolution powers of Motzkin numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results Liu, Feihu Wang, Ying Zhang, Yingrui Zhang, Zihao Combinatorics Cigler considered certain shifted Hankel determinants of convolution powers of Catalan numbers and conjectured identities for these determinants. Recently, Fulmek gave a bijective proof of Cigler's conjecture. Cigler then provided a computational proof. We extend Cigler's determinant identities to the convolution of general power series $F(x)$, where $F(x)$ satisfies a certain type of quadratic equation. As an application, we present the Hankel determinant identities of convolution powers of Motzkin numbers. |
| title | Hankel Determinants for Convolution of Power Series: An Extension of Cigler's Results |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.17187 |