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IDENTITIES FOR 3-CORE AND 5-CORE PARTITIONS

박윤경
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회지 (Journal of the KMS)|제51권 제2호|pp. 225-238

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참고문헌

키워드

modular functions.t-cores
주제분류수학

초록

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

Abstract

We apply modular function theory to find the relation among t-core partitions. By using the generators of function field corresponding to a certain modular group, we reprove the identities in [1] because their relations are linear for t = 3 or 5.

참고문헌 (10)

  1. N. Baruah, "Partition identities and Ramanujan's modular equations", J. Combin. Theory Ser. A, 114(6), pp.1024~1045 (2007)
  2. A. Berkovich, "New identities for 7-cores with prescribed BG-rank", Discrete Math, 308(22), pp.5246~5259 (2008)
  3. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  4. B. Cho, "Arithmetic of the Ramanujan-Gollnitz-Gordon continued fraction", J. Number Theory, 129(4), pp.922~947 (2009)
  5. F. Garvan, "Cranks and t-cores", Invent. Math, 101(1), pp.1~17 (1990)
  6. M. D. Hirschhorn, "Elementary proofs of various facts about 3-cores", Bull. Aust. Math. Soc, 79(3), pp.507~512 (2009)
  7. N. Ishida, "The equations for modular function fields of principal congruence subgroups of prime level", Manuscripta Math, 90(3), pp.271~285 (1996)
  8. B. Kim, "On inequalities and linear relations for 7-core partitions", Discrete Math, 310(4), pp.861~868 (2010)
  9. D. Kubert, "Modular Units" (1981), Springer-Verlag
  10. S. Ramanujan, "Notebooks (2 volumes)" (1957), Tata Institute of Fundamental Research

관련 논문AI추천

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