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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.13693 |
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| _version_ | 1866912201450717184 |
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| author | Marques, Sophie Mrema, Elizabeth |
| author_facet | Marques, Sophie Mrema, Elizabeth |
| contents | This paper examines the recursive sequence of polynomials $p_n(x)$, defined by $p_0(x) = x^2 - 2$ and $p_n(x) = p_{n-1}(x)^2 - 2$ for $n \geq 1$. It describes the field-theoretic motivations behind this sequence, derives a recursive formula for its coefficients, and identifies invariants that uncover combinatorial connections, including links to weighted Catalan numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A study of a recursive sequence of polynomials revealing weighted Catalan Numbers Marques, Sophie Mrema, Elizabeth Combinatorics Number Theory This paper examines the recursive sequence of polynomials $p_n(x)$, defined by $p_0(x) = x^2 - 2$ and $p_n(x) = p_{n-1}(x)^2 - 2$ for $n \geq 1$. It describes the field-theoretic motivations behind this sequence, derives a recursive formula for its coefficients, and identifies invariants that uncover combinatorial connections, including links to weighted Catalan numbers. |
| title | A study of a recursive sequence of polynomials revealing weighted Catalan Numbers |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2501.13693 |