Efficient calculation of the number of partitions of the set into subsets satisfying
Consider the set [Formula: see text]. We are interested in determining the number of partitions of this set into subsets of three elements each, where the sum of two of the elements equals the third. To achieve this, we provide a set of criteria that must be met by any valid partition. These criteri...
| Published in: | Mathematics Open |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2024-01-01
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| Online Access: | https://www.worldscientific.com/doi/10.1142/S2811007224500056 |
| _version_ | 1850026773443510272 |
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| author | Christian Hercher Frank Niedermeyer |
| author_facet | Christian Hercher Frank Niedermeyer |
| author_sort | Christian Hercher |
| collection | DOAJ |
| container_title | Mathematics Open |
| description | Consider the set [Formula: see text]. We are interested in determining the number of partitions of this set into subsets of three elements each, where the sum of two of the elements equals the third. To achieve this, we provide a set of criteria that must be met by any valid partition. These criteria then can be used for efficient pruning in the search for these partitions. Specifically, we enumerate all such partitions for [Formula: see text] and [Formula: see text], and added these new terms to the series A108235 in the Online Encyclopedia of Integer Sequences. |
| format | Article |
| id | doaj-art-8fea3f4d5aeb47ee82faec9c4aeca7ae |
| institution | Directory of Open Access Journals |
| issn | 2811-0072 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| spelling | doaj-art-8fea3f4d5aeb47ee82faec9c4aeca7ae2025-08-20T00:37:43ZengWorld Scientific PublishingMathematics Open2811-00722024-01-010310.1142/S2811007224500056Efficient calculation of the number of partitions of the set into subsets satisfyingChristian Hercher0Frank Niedermeyer1Institut für Mathematik, Europa-Universität Flensburg, Auf dem Campus 1b, 24943 Flensburg, GermanyBonn, GermanyConsider the set [Formula: see text]. We are interested in determining the number of partitions of this set into subsets of three elements each, where the sum of two of the elements equals the third. To achieve this, we provide a set of criteria that must be met by any valid partition. These criteria then can be used for efficient pruning in the search for these partitions. Specifically, we enumerate all such partitions for [Formula: see text] and [Formula: see text], and added these new terms to the series A108235 in the Online Encyclopedia of Integer Sequences.https://www.worldscientific.com/doi/10.1142/S2811007224500056Set partitions with arithmetic property |
| spellingShingle | Christian Hercher Frank Niedermeyer Efficient calculation of the number of partitions of the set into subsets satisfying Set partitions with arithmetic property |
| title | Efficient calculation of the number of partitions of the set into subsets satisfying |
| title_full | Efficient calculation of the number of partitions of the set into subsets satisfying |
| title_fullStr | Efficient calculation of the number of partitions of the set into subsets satisfying |
| title_full_unstemmed | Efficient calculation of the number of partitions of the set into subsets satisfying |
| title_short | Efficient calculation of the number of partitions of the set into subsets satisfying |
| title_sort | efficient calculation of the number of partitions of the set into subsets satisfying |
| topic | Set partitions with arithmetic property |
| url | https://www.worldscientific.com/doi/10.1142/S2811007224500056 |
| work_keys_str_mv | AT christianhercher efficientcalculationofthenumberofpartitionsofthesetintosubsetssatisfying AT frankniedermeyer efficientcalculationofthenumberofpartitionsofthesetintosubsetssatisfying |