Partition identities from third and sixth order mock theta functions

Agarwal, 1998, Lattice paths and n-color partitions, Util. Math., 53, 71 Agarwal, 2002, n-colour partitions, 301 Agarwal, 2004, n-color partition theoretic interpretations of some mock theta functions, Electron. J. Combin., 11, 10.37236/1855 Agarwal, 1987, Rogers–Ramanujan identities for partitions with n copies of n, J. Combin. Theory Ser. A, 45, 40, 10.1016/0097-3165(87)90045-8 Agarwal, 1989, Lattice paths and multiple basic hypergeometric series, Pacific J. Math., 136, 209, 10.2140/pjm.1989.136.209 Andrews, 2009 Andrews, 1989, Ramanujan’s Lost notebook. VI. The mock theta conjectures, Adv. Math., 73, 242, 10.1016/0001-8708(89)90070-4 Andrews, 1991, Ramanujan’s Lost notebook VII: the sixth order mock theta functions, Adv. Math., 89, 60, 10.1016/0001-8708(91)90083-J Berndt, 2006 Berndt, 2007, Sixth order mock theta functions, Adv. Math., 216, 771, 10.1016/j.aim.2007.06.004 Berndt, 1995, vol. 9 Chan, 2010, Ramanujan’s cubic continued fraction and an analog of his “most beautiful identity”, Int. J. Number Theory, 6, 673, 10.1142/S1793042110003150 Chan, 2010, Ramanujan’s cubic continued fraction and Ramanujan type congruences for a certain partition function, Int. J. Number Theory, 6, 819, 10.1142/S1793042110003241 Chan, 2011, Distribution of a certain partition function modulo powers of primes, Acta Math. Sin. (Engl. Ser.), 27, 625, 10.1007/s10114-011-8620-2 Chan, 2010, New analogues of Ramanujan’s partition identities, J. Number Theory, 130, 1898, 10.1016/j.jnt.2010.02.017 W. Chen, B. Lin, Congruences for the number of cubic partitions derived from modular forms, Preprint. Choi, 2000, Tenth order mock theta functions in Ramanujan’s lost notebook (II), Adv. Math., 156, 180, 10.1006/aima.2000.1948 Choi, 2006, Tenth order mock theta functions in Ramanujan’s lost notebook III, Proc. Lond. Math. Soc. (3), 94, 26, 10.1112/plms/pdl006 Choi, 2011, The basic bilateral hypergeometric series and the mock theta functions, Ramanujan J., 24, 345, 10.1007/s11139-010-9269-7 Fine, 1988, vol. 27 Garvan, 1990, Cranks and t-cores, Invent. Math., 101, 1, 10.1007/BF01231493 Gordon, 1981, Ramanujan congruences for q(n), vol. 899, 333 Gordon, 2011, A survey of classical mock theta functions, vol. 23 D. Hickerson, Personal communication to G.E. Andrews, 2000. Kim, 2010, The overcubic partition mod 3, vol. 14, 157 Kim, 2011, A crank analog on a certain kind of partition function arising from the cubic continued fraction, Acta Arith., 148, 1, 10.4064/aa148-1-1 Knopp, 1993 G. Ligozat, Courbes modulaires de genre 1, Bull. Soc. Math. France, Mém. 43. Supplément au Bull. Soc. Math. France Tome 103, no. 3. Société Mathématique de France, Paris, 1975. 80 pp. Lovejoy, 2008, n-color overpartitions, twisted divisor functions, and Rogers–Ramanujan identities, South East Asian J. Math. Math. Sci., 6, 23 R.J. McIntosh, Modular transformations of Ramanujan’s sixth order mock theta functions, Preprint. Newman, 1959, Construction and application of a class of modular functions II, Proc. Lond. Math. Soc. (3), 9, 373, 10.1112/plms/s3-9.3.373 Ono, 2004, Web of modularity: arithmetic of the coefficients of modular forms and q-series Ono, 2009, Unearthing the visions of a master: harmonic Maass forms and number theory, 347 Ramanujan, 1988 Rankin, 1977 Z. Reti, Five problems in combinatorial number theory, Ph.D. Thesis, University of Florida, 1994. Robbins, 2000, On t-core partitions, The Fibonacci Quarterly, 38, 39 Robins, 1994, Generalized Dedekind η-products, Contemp. Math., 166, 119, 10.1090/conm/166/01645 Sinick, 2010, Ramanujan congruences for a class of eta quotients, Int. J. Number Theory, 6, 835, 10.1142/S1793042110003253 Watson, 1936, The final problem: an account of the mock theta functions, J. Lond. Math. Soc., 11, 55, 10.1112/jlms/s1-11.1.55