An Investigation on Partitions with Equal Products
Fuente:
arXiv
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| Autores principales: | , , , , , , , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866911016542011392 |
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| author | Cha, Byungchul Claman, Adam Harrington, Joshua Liu, Ziyu Maldonado, Barbara Miller, Alexander Palma, Ann Wong, Tony W. H. Yi, Hongkwon V. |
| author_facet | Cha, Byungchul Claman, Adam Harrington, Joshua Liu, Ziyu Maldonado, Barbara Miller, Alexander Palma, Ann Wong, Tony W. H. Yi, Hongkwon V. |
| contents | An ordered triple $(s,p,n)$ is called admissible if there exist two different multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that $X$ and $Y$ share the same sum $s$, the same product $p$, and the same size $n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is admissible. Finally, we consider the situation where $r$ different multisets are needed, instead of just two. This project is also related to John Conway's wizard puzzle from the 1960s. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_07451 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An Investigation on Partitions with Equal Products Cha, Byungchul Claman, Adam Harrington, Joshua Liu, Ziyu Maldonado, Barbara Miller, Alexander Palma, Ann Wong, Tony W. H. Yi, Hongkwon V. Number Theory Combinatorics 05A17, 11B75, 11B83 An ordered triple $(s,p,n)$ is called admissible if there exist two different multisets $X=\{x_1,x_2,\dotsc,x_n\}$ and $Y=\{y_1,y_2,\dotsc,y_n\}$ such that $X$ and $Y$ share the same sum $s$, the same product $p$, and the same size $n$. We first count the number of $n$ such that $(s,p,n)$ are admissible for a fixed $s$. We also fully characterize the values $p$ such that $(s,p,n)$ is admissible. Finally, we consider the situation where $r$ different multisets are needed, instead of just two. This project is also related to John Conway's wizard puzzle from the 1960s. |
| title | An Investigation on Partitions with Equal Products |
| topic | Number Theory Combinatorics 05A17, 11B75, 11B83 |
| url | https://arxiv.org/abs/1811.07451 |