Congruences involving F-partition functions
The primary goal of this note is to prove the congruence ϕ3(3n+2)≡0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors.
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| Format: | Article |
| Language: | English |
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Wiley
1994-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171294000256 |
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| _version_ | 1832560436278460416 |
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| author | James Sellers |
| author_facet | James Sellers |
| author_sort | James Sellers |
| collection | DOAJ |
| description | The primary goal of this note is to prove the congruence ϕ3(3n+2)≡0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors. |
| format | Article |
| id | doaj-art-2ef4fa5b80c44efd88c72ed84dd41919 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1994-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2ef4fa5b80c44efd88c72ed84dd419192025-02-03T01:27:36ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251994-01-0117118718810.1155/S0161171294000256Congruences involving F-partition functionsJames Sellers0Department of Science and Mathematics, Cedarville College, Cedarville 45314, OH, USAThe primary goal of this note is to prove the congruence ϕ3(3n+2)≡0(mod3), where ϕ3(n) denotes the number of F-partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F-partitions of n with 2 colors.http://dx.doi.org/10.1155/S0161171294000256congruencepartitions. |
| spellingShingle | James Sellers Congruences involving F-partition functions International Journal of Mathematics and Mathematical Sciences congruence partitions. |
| title | Congruences involving F-partition functions |
| title_full | Congruences involving F-partition functions |
| title_fullStr | Congruences involving F-partition functions |
| title_full_unstemmed | Congruences involving F-partition functions |
| title_short | Congruences involving F-partition functions |
| title_sort | congruences involving f partition functions |
| topic | congruence partitions. |
| url | http://dx.doi.org/10.1155/S0161171294000256 |
| work_keys_str_mv | AT jamessellers congruencesinvolvingfpartitionfunctions |