논문KCI 등재
Cubic partition pairs weighted by the parity of the crank
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We study congruence properties of the number of cubic partition pairs weighted by the parity of the crank. If we define such number to be $c(n)$, then \[ c(5n+4) \equiv 0 \pmod{5} \;\; \text{ and } \;\; c(7n+2) \equiv 0 \pmod{7}, \] for all nonnegative integers $n$.
Abstract
We study congruence properties of the number of cubic partition pairs weighted by the parity of the crank. If we define such number to be $c(n)$, then \[ c(5n+4) \equiv 0 \pmod{5} \;\; \text{ and } \;\; c(7n+2) \equiv 0 \pmod{7}, \] for all nonnegative integers $n$.
참고문헌 (9)
- G.E. Andrews, "Dyson's crank of a partition", Bull. Amer. Math. Soc, 18, pp.167~171 (1988)
- B.C. Berndt, "Number theory in the spirit of Ramanujan" (2006), American Mathematical Society
- H.-C. Chan, "Ramanujan's cubic continued fraction and an analog of his "most beautiful identity"", Int. J. Number Thy, 6, pp.673~680 (2010)
- H.-C. Chan, "Ramanujan's cubic continued fraction and Ramanujan type congru-ences for a certain partition function", Int. J. Number Thy, 6, pp.819~834 (2010)
- H.-C. Chan, "Distribution of a certain partition function modulo powers of primes", Acta Math. Sin. (Engl. Ser.), 27, pp.625~634 (2011)
- D. Choi, "Partitions weighted by the parity of the crank", J. Combin. Theory Ser. A, 116, pp.1034~1046 (2009)
- B. Kim, "A crank analog on a certain kind of partition function arising from the cubic continued fraction", Acta. Arith, 148, pp.1~19 (2011)
- B. Kim, "Partition Statistics for cubic partition pairs", Electronic J. of Combina-torics, 18, pp.128~ (2011)
- H. Zhao, "Ramanujan type congruences for a certain partition function", Electronic J. of Combinatorics, 18, pp.58~ (2011)
관련 논문AI추천
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