Computer-aided solution to the $k$-bonacci pick-up sticks problem
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908484455366656 |
|---|---|
| author | Kern, Julian |
| author_facet | Kern, Julian |
| contents | A full solution to the recently proposed problem of determining the probability that no $k$-gon can be built from $n$ independently and uniformly chosen sticks in $[0,1]$ is proposed. This extends the known results for triangles and quadrilaterals to general $k$-gons and offers a clearer interpretation of the connection to products of $k$-bonacci numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Computer-aided solution to the $k$-bonacci pick-up sticks problem Kern, Julian Combinatorics Probability 60C05 (Primary) 11B39, 52B11, 62G30 (Secondary) A full solution to the recently proposed problem of determining the probability that no $k$-gon can be built from $n$ independently and uniformly chosen sticks in $[0,1]$ is proposed. This extends the known results for triangles and quadrilaterals to general $k$-gons and offers a clearer interpretation of the connection to products of $k$-bonacci numbers. |
| title | Computer-aided solution to the $k$-bonacci pick-up sticks problem |
| topic | Combinatorics Probability 60C05 (Primary) 11B39, 52B11, 62G30 (Secondary) |
| url | https://arxiv.org/abs/2508.07943 |