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Congruences modulo 7 and 11 for (s,t)-regular bipartitions

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Let Bs,t(n) denote the number of (s, t)-regular bipartitions of n. In this paper, we prove several infinite families of congruences modulo s for Bs,t(n), where (s, t)∈{(7, 5), (7, 25) (7, 125), (11, 5)}.

Abstract

Let Bs,t(n) denote the number of (s, t)-regular bipartitions of n. In this paper, we prove several infinite families of congruences modulo s for Bs,t(n), where (s, t)∈{(7, 5), (7, 25) (7, 125), (11, 5)}.

참고문헌 (16)

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  2. C. Adiga, "Some new congruences for (s, t)-regular bi-partition functions", Publ. Inst. Math. (2017)
  3. C. Adiga, "Congruences for 7 and 49-regular partitions modulo powers of 7", Ramanujan .J. (2017)[DOI]
  4. B.C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006)
  5. D.Q.J. Dou, "Congruences for (3, 11)-regular bipartitions modulo 11", Ramanujan J., 40(3), pp.535~540 (2016)[DOI]
  6. B.L.S. Lin, "Arithmetic of the 7-regular bipartition function modulo 3", Ramanujan J., 37, pp.469~478 (2015)[DOI]
  7. B.L.S. Lin, "An infinite family of congruences modulo 3 for 13-regular bipartitions", Ramanujan J., 39, pp.169~178 (2016)[DOI]
  8. S. Ramanujan, "Collected Papers" (1927), Cambridge University Press
  9. S. Ramanujan, "Some propeties of p(n), the number of partitions of n", Proc. Cambridge Philos. Soc., 19, pp.207~210 (1919)
  10. D. Ranganatha, "On a Ramanujan-type congruence for bipartitions with 5-cores", J. Integer Sequences, 19 (2016)
  11. D. Ranganatha, "Ramanujan-type congruences modulo powers of 5 and 7", Indian J. Pure Appl. Math., 48(3), pp.449~465 (2017)[DOI]
  12. G.N. Watson, "Ramanujan's Vermutung uber Zerfallungsanzahlem", J. reine angew. Math., 179, pp.97~128 (1938)
  13. G.N. Watson, "Theorems stated by Ramanujan (VII): theorems on contuined fractions", J. London Math. Soc., 4, pp.39~48 (1929)
  14. L. Wang, "Congruences modulo powers of 5 for two restricted bipartitions", Ramanujan J., 44(3), pp.471~491 (2017)[DOI]
  15. E.X.W. Xia, "Congruences for some <TEX>$\ell$<", TEX>-regular partitions modulo <TEX>$\ell$<, J. Number Theory, pp.2015, 152[DOI]
  16. E.X.W. Xia, "Arithmetic properties for (s,t)-regular bipartition functions", J. Number Theory, 171, pp.1~17 (2017)[DOI]

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