Computational proofs of congruences for 2-colored Frobenius partitions
In 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202007342 |
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| author | Dennis Eichhorn James A. Sellers |
| author_facet | Dennis Eichhorn James A. Sellers |
| author_sort | Dennis Eichhorn |
| collection | DOAJ |
| description | In 1994, the following infinite family of congruences was
conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α.
In this paper, the first four cases of this family are proved. |
| format | Article |
| id | doaj-art-843f5c5da6cd454683b4575d6d2c5a5b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-843f5c5da6cd454683b4575d6d2c5a5b2025-02-03T01:31:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0129633334010.1155/S0161171202007342Computational proofs of congruences for 2-colored Frobenius partitionsDennis Eichhorn0James A. Sellers1Department of Mathematics, University of Arizona, Tucson, AZ 85721, USADepartment of Mathematics, Penn State University, University Park, PA 16802, USAIn 1994, the following infinite family of congruences was conjectured for the partition function cΦ2(n) which counts the number of 2-colored Frobenius partitions of n: for all n≥0 and α≥1, cΦ2(5αn+λα)≡0(mod5α), where λα is the least positive reciprocal of 12 modulo 5α. In this paper, the first four cases of this family are proved.http://dx.doi.org/10.1155/S0161171202007342 |
| spellingShingle | Dennis Eichhorn James A. Sellers Computational proofs of congruences for 2-colored Frobenius partitions International Journal of Mathematics and Mathematical Sciences |
| title | Computational proofs of congruences for 2-colored Frobenius partitions |
| title_full | Computational proofs of congruences for 2-colored Frobenius partitions |
| title_fullStr | Computational proofs of congruences for 2-colored Frobenius partitions |
| title_full_unstemmed | Computational proofs of congruences for 2-colored Frobenius partitions |
| title_short | Computational proofs of congruences for 2-colored Frobenius partitions |
| title_sort | computational proofs of congruences for 2 colored frobenius partitions |
| url | http://dx.doi.org/10.1155/S0161171202007342 |
| work_keys_str_mv | AT denniseichhorn computationalproofsofcongruencesfor2coloredfrobeniuspartitions AT jamesasellers computationalproofsofcongruencesfor2coloredfrobeniuspartitions |