[1] | Alladi, K.; Andrews, G. E.; Gordon, B., Refinements and generalizations of Capparelli’s conjecture on partitions, J. Algebra, 174, 636-658 (1995) ·Zbl 0830.05005 |
[2] | Andrews, G. E., The Theory of Partitions, Encyclopedia Math. Appl., vol. 2 (1998), Addison-Wesley: Cambridge Univ. Press, Reissued ·Zbl 0906.05004 |
[3] | Andrews, G. E., Multiple series Rogers-Ramanujan type identities, Pacific J. Math., 114, 267-283 (1984) ·Zbl 0547.10012 |
[4] | Andrews, G. E., Generalized Frobenius partitions, Mem. Amer. Math. Soc., 49, 301 (1984) ·Zbl 0544.10010 |
[5] | Andrews, G. E., \(q\)-Series: Their Development and Application in Analysis, Number Theory, Combinatorics, Physics, and Computer Algebra, CBMS Reg. Conf. Ser. Math., vol. 66 (1986), Amer. Math. Soc: Amer. Math. Soc Providence, RI ·Zbl 0594.33001 |
[6] | Andrews, G. E., Schur’s theorem, Capparelli’s conjecture and \(q\)-trinomial coefficients, (Proc. Rademacher Centenary Conf., 1992. Proc. Rademacher Centenary Conf., 1992, Contemp. Math., vol. 166 (1994), Amer. Math. Soc: Amer. Math. Soc Providence, RI), 141-154 ·Zbl 0811.05001 |
[7] | G.E. Andrews, private communication, August 18, 2003; G.E. Andrews, private communication, August 18, 2003 |
[8] | Bailey, W. N., Some identities in combinatory analysis, Proc. London Math. Soc. (2), 49, 421-425 (1947) ·Zbl 0041.03403 |
[9] | Bailey, W. N., On identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2), 50, 1-10 (1948) ·Zbl 0031.39203 |
[10] | S. Capparelli, Vertex operator relations for affine Lie algebras and combinatorial identities, PhD thesis, Rutgers, 1988; S. Capparelli, Vertex operator relations for affine Lie algebras and combinatorial identities, PhD thesis, Rutgers, 1988 |
[11] | Capparelli, S., A construction of the level 3 modules for the affine algebra \(A_2^{(2)}\) and a new combinatorial identity of the Rogers-Ramanujan type, Trans. Amer. Math. Soc., 348, 2, 481-501 (1996) ·Zbl 0862.17017 |
[12] | Gasper, G.; Rahman, M., Basic Hypergeometric Series (1990), Cambridge Univ. Press ·Zbl 0695.33001 |
[13] | H. Göllnitz, Einfache partitionen, Diplomarbeit W.S., Göttingen, 1960; H. Göllnitz, Einfache partitionen, Diplomarbeit W.S., Göttingen, 1960 |
[14] | Gordon, B., Some continued fractions of the Rogers-Ramanujan type, Duke J., 31, 741-748 (1965) ·Zbl 0178.33404 |
[15] | Lepowsky, J.; Milne, S. C., Lie algebraic approaches to classical partition identities, Adv. Math., 29, 1, 15-59 (1978) ·Zbl 0384.10008 |
[16] | Lepowsky, J.; Milne, S. C., Lie algebras and classical partition identities, Proc. Natl. Acad. Sci. USA, 75, 2, 578-579 (1978) ·Zbl 0379.17003 |
[17] | Lepowsky, J.; Wilson, R. L., Construction of the affine Lie algebra \(A_1^{(1)}\), Commun. Math. Phys., 62, 43-53 (1978) ·Zbl 0388.17006 |
[18] | Lepowsky, J.; Wilson, R. L., The Rogers-Ramanujan identities: Lie theoretic interpretation and proof, Proc. Natl. Acad. Sci. USA, 78, 699-701 (1981) ·Zbl 0449.17010 |
[19] | Lepowsky, J.; Wilson, R. L., A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Adv. Math., 45, 21-72 (1982) ·Zbl 0488.17006 |
[20] | Lepowsky, J.; Wilson, R. L., A new family of algebras underlying the Rogers-Ramanujan identities and generalizations, Invent. Math., 77, 199-290 (1984) ·Zbl 0577.17009 |
[21] | Lepowsky, J.; Wilson, R. L., The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities, Invent. Math., 79, 417-442 (1985) ·Zbl 0577.17010 |
[22] | MacMahon, P. A., Combinatory Analysis, vol. 2 (1918), Cambridge Univ. Press ·JFM 46.0118.07 |
[23] | Meurman, A.; Primc, M., A basis of the basic \(sl(3,C)^~\)-module, Commun. Contemp. Math., 3, 4, 593-614 (2001) ·Zbl 1004.17003 |
[24] | Petkovšek, M.; Wilf, H.; Zeilberger, D., \(A=B (1996)\), Peters ·Zbl 0848.05002 |
[25] | Propp, J., Some variants of Ferrers diagrams, J. Combin. Theory A, 52, 98-128 (1989) ·Zbl 0682.05007 |
[26] | Rogers, L. J., Second memoir on the expansion of certain infinite products, Proc. London Math. Soc., 25, 318-343 (1894) |
[27] | Schur, I., (Ein Beitrag zur additeven Zahlentheorie und zur Theorie der Kettenbrüche (1917), Sitz.ber. Berlin. Akad), 302-321 ·JFM 46.0201.01 |
[28] | Slater, L. J., Further identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (2), 54, 147-167 (1952) ·Zbl 0046.27204 |
[29] | Tamba, M.; Xie, C., Level three standard modules for \(A_2^{(2)}\) and combinatorial identities, J. Pure Appl. Algebra, 105, 1, 53-92 (1995) ·Zbl 0854.17029 |