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ARITHMETIC PROPERTIES OF PARTITIONS WITH 5-CORES

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Let a5(n) denote the number of partitions of n that are 5-cores. By using theta function identities, we find several infinite families of congruences modulo 3, 4 and 8 for a5(n).

Abstract

Let a5(n) denote the number of partitions of n that are 5-cores. By using theta function identities, we find several infinite families of congruences modulo 3, 4 and 8 for a5(n).

참고문헌 (14)

  1. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  2. S. C. Chen, "Congruences for t-core partition functions", J. Number Theory, 133, pp.4036~4046 (2013)[DOI]
  3. K. Das, "Conqruences modulo 3 for two interesting partitions arising from two theta function identities", Note di Mat., 36(2), pp.61~76 (2016)
  4. F. Garvan, "Cranks and t-cores", Invent. Math., 101, pp.1~17 (1990)[DOI]
  5. A. Granville, "Defect zero p-blocks for finite simple groups", Trans. Amer. Math. Soc., 348(1), pp.331~347 (1996)[DOI]
  6. M. D. Hirschhorn, "Some amazing facts about 4-cores", J. Number Theory, 60, pp.51~69 (1996)[DOI]
  7. M. D. Hirschhorn, "Elementary proofs of various facts about 8-cores", Bull. Aust. Math. Soc., 79(3), pp.507~512 (2009)[DOI]
  8. M. D. Hirschhorn, "Elementary proofs of parity results for 5-regular partitions", Bull. Aust. Math. Soc., 81, pp.58~63 (2010)[DOI]
  9. J. Liu, "Arithmetic Properties of a restricted bipartition function", The Electronic Journal of Combinatorics, 22(3), pp.3.8~ (2015)
  10. M. S. M. Naika, "Color partitions identities arising from Ramanujan's theta-functions", Acta Math. Vietnam., 41, pp.633~660 (2016)[DOI]
  11. S. Radu, "Parity results for broken k-diamond partitions and (2k+1)-cores", Acta Arith., 146, pp.43~52 (2011)[DOI]
  12. S. Ramanujan, "Collected papers" (1927), Cambridge university press
  13. S. Ramanujan, "The lost notebook and other unpublished papers" (1988), Narosa
  14. E. X. W. Xia, "Ramanujan-type congruences modulo 8 for 7- and 23-core partition functions", Ramanujan J.[DOI]

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