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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21785 |
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| _version_ | 1866909976033755136 |
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| author | Rubine, Dean |
| author_facet | Rubine, Dean |
| contents | The closed form for the hyper-Catalan number C[m2,m3,m4,...], which counts the number of subdivisions of a roofed polygon into m2 triangles, m3 quadrilaterals, m4 pentagons, etc., has been known since 1940. In 2025, Wildberger and Rubine showed its generating series S[t2,t3,t4,...] is a zero of the general geometric univariate polynomial. They note the factorization S=(t2 + t3 + t4 + ...)G, where the factor G is called the Geode. Later in 2025, Amderberhan, Kauers and Zeilberger issued a challenge to compute G[1000,1000,1000,1000], the coefficient of $t_2^{1000}t_3^{1000}t_4^{1000}t_5^{1000}$ in G. The reward is a donation to OEIS. We describe the computation, give the value and claim the reward. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21785 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computing the 4D Geode Rubine, Dean Combinatorics 05A15 The closed form for the hyper-Catalan number C[m2,m3,m4,...], which counts the number of subdivisions of a roofed polygon into m2 triangles, m3 quadrilaterals, m4 pentagons, etc., has been known since 1940. In 2025, Wildberger and Rubine showed its generating series S[t2,t3,t4,...] is a zero of the general geometric univariate polynomial. They note the factorization S=(t2 + t3 + t4 + ...)G, where the factor G is called the Geode. Later in 2025, Amderberhan, Kauers and Zeilberger issued a challenge to compute G[1000,1000,1000,1000], the coefficient of $t_2^{1000}t_3^{1000}t_4^{1000}t_5^{1000}$ in G. The reward is a donation to OEIS. We describe the computation, give the value and claim the reward. |
| title | Computing the 4D Geode |
| topic | Combinatorics 05A15 |
| url | https://arxiv.org/abs/2512.21785 |