Some congruences for 3-component multipartitions
Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 fo...
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De Gruyter
2016-01-01
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| Series: | Open Mathematics |
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| Online Access: | http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0067/math-2016-0067.xml?format=INT |
| _version_ | 1818446477228244992 |
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| author | Zhao Tao Yan Jin Lily J. Gu C. |
| author_facet | Zhao Tao Yan Jin Lily J. Gu C. |
| author_sort | Zhao Tao Yan |
| collection | DOAJ |
| description | Let p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310). |
| first_indexed | 2024-12-14T19:48:21Z |
| format | Article |
| id | doaj.art-3724370bd2ea47629156934f02b840f4 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-14T19:48:21Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-3724370bd2ea47629156934f02b840f42022-12-21T22:49:31ZengDe GruyterOpen Mathematics2391-54552016-01-0114178378810.1515/math-2016-0067math-2016-0067Some congruences for 3-component multipartitionsZhao Tao Yan0Jin Lily J.1Gu C.2Department of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, ChinaSchool of Mathematics, Nanjing Normal University, Taizhou College, Jiangsu, Taizhou 225300, ChinaDepartment of Mathematics, Jiangsu University, Jiangsu, Zhenjiang 212013, ChinaLet p3(n) denote the number of 3-component multipartitions of n. Recently, using a 3-dissection formula for the generating function of p3(n), Baruah and Ojah proved that for n ≥ 0, p3(9n + 5) ≡ 0 (mod 33) and p3 (9n + 8) ≡ 0 (mod 34). In this paper, we prove several congruences modulo powers of 3 for p3(n) by using some theta function identities. For example, we prove that for n ≥ 0, p3 (243n + 233) ≡ p3 (729n + 638) ≡ 0 (mod 310).http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0067/math-2016-0067.xml?format=INTcongruencesmultipartitionstheta functions11p8305a17 |
| spellingShingle | Zhao Tao Yan Jin Lily J. Gu C. Some congruences for 3-component multipartitions Open Mathematics congruences multipartitions theta functions 11p83 05a17 |
| title | Some congruences for 3-component multipartitions |
| title_full | Some congruences for 3-component multipartitions |
| title_fullStr | Some congruences for 3-component multipartitions |
| title_full_unstemmed | Some congruences for 3-component multipartitions |
| title_short | Some congruences for 3-component multipartitions |
| title_sort | some congruences for 3 component multipartitions |
| topic | congruences multipartitions theta functions 11p83 05a17 |
| url | http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0067/math-2016-0067.xml?format=INT |
| work_keys_str_mv | AT zhaotaoyan somecongruencesfor3componentmultipartitions AT jinlilyj somecongruencesfor3componentmultipartitions AT guc somecongruencesfor3componentmultipartitions |