Acknowledgement
The author appreciate the anonymous referee for valuable suggestions and very careful reading, which improve the exposition of the paper a lot.
References
- G.E. Andrews, The Theory of Partitions, Addison-Wesley, Reading, MA, 1976; reissued: Cambridge University Press, Cambridge, 1998.
- G.E. Andrews and F. Garvan, Dyson's crank of a partition, Bull. Amer. Math. Soc. 18 (1988) (2), 167-171. https://doi.org/10.1090/S0273-0979-1988-15637-6
- A.O.L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. 4 (1954), 84-106.
- B.C. Berndt, Number theory in the spirit of Ramanujan, Student Mathematical Library, 34. American Mathematical Society, Providence, RI, 2006.
- F.J. Dyson, Some guesses in the theory of partitions, Eureka 8 (1944), 10-15.
- F. Garvan, New combinatorial interpretations of Ramanujan's partition congruences mod 5, 7 and 11, Trans. Amer. Math. Soc. 305 (1988), no. 1, 47-77. https://doi.org/10.1090/S0002-9947-1988-0920146-8
- B. Kim, Group Actions on Partitions, Elect. J. Comb. 24 (2017), Paper #P3.58.
- B. Kim, Polygonal partitions, Korean J. Math. 26 (2018), no. 2, 167-174. https://doi.org/10.11568/KJM.2018.26.2.167