Efficient Calculation the Number of Partitions of the Set $\{1, 2, \ldots, 3n\}$ into Subsets $\{x, y, z\}$ Satisfying $x+y=z$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914894827225088 |
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| author | Hercher, Christian Niedermeyer, Frank |
| author_facet | Hercher, Christian Niedermeyer, Frank |
| contents | Consider the set $\{1,2,\ldots,3n\}$. We are interested in the number of partitions of this set into subsets of three elements each, where the sum of two of them equals the third.
We give some criteria such a partition has to fulfill, which can be used for efficient pruning in the search for these partitions. In particular, we enumerate all such partitions for $n=16$ and $n=17$ adding new terms to the series A108235 in the Online Encyclopedia of Integer Sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00303 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Calculation the Number of Partitions of the Set $\{1, 2, \ldots, 3n\}$ into Subsets $\{x, y, z\}$ Satisfying $x+y=z$ Hercher, Christian Niedermeyer, Frank Combinatorics 05A18 Consider the set $\{1,2,\ldots,3n\}$. We are interested in the number of partitions of this set into subsets of three elements each, where the sum of two of them equals the third. We give some criteria such a partition has to fulfill, which can be used for efficient pruning in the search for these partitions. In particular, we enumerate all such partitions for $n=16$ and $n=17$ adding new terms to the series A108235 in the Online Encyclopedia of Integer Sequences. |
| title | Efficient Calculation the Number of Partitions of the Set $\{1, 2, \ldots, 3n\}$ into Subsets $\{x, y, z\}$ Satisfying $x+y=z$ |
| topic | Combinatorics 05A18 |
| url | https://arxiv.org/abs/2307.00303 |