Plane partitions. III: The weak Macdonald conjecture. (English) Zbl 0421.10011

Andrews, George E.

Invent. Math. 53, 193-225 (1979).

MSC:

11P81

Elementary theory of partitions

Keywords:

plane partition; MacMahon conjecture; Ferrers graph; limiting Macdonald conjecture; weak Macdonald conjecture; descending plane partitions conjecture

Citations:

Zbl 0376.10014

References:

[1]	Andrews, G.E.: MacMahon’s conjecture on symmetric plane partitions. Proc. Nat. Acad. Sci. USA,74, 426-429 (1977) · Zbl 0353.05006 · doi:10.1073/pnas.74.2.426
[2]	Andrews, G.E.: Plane partitions (II): the equivalence of the Bender-Knuth and MacMahon conjectures. Pac. J. Math.,72, 283-291 (1977) · Zbl 0376.10014
[3]	Andrews, G.E.: The Theory of Partitions, Addision-Wesley, Reading, 1976 · Zbl 0371.10001
[4]	Andrews, G.E.: Plane partitions (I): the MacMahon conjecture, Advances in Math. (to appear) · Zbl 0462.10010
[5]	Andrews, G.E.: On Macdonald’s conjecture and descending plane partitions, Proceedings of the Alfred Young Day Conference (to appear) · Zbl 0441.05005
[6]	Askey, R., Wilson, J.: A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols, S.I.A.M. J. Math. Anal., (to appear) · Zbl 0437.33014
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[9]	Gansner, E.: Matrix correspondences and the enumeration of plane partitions, Ph.D. Thesis, M.I.T., 1978
[10]	Macdonald, I.G.: Lecture on plane partitions, Oberwolfach Conference on Combinatorics and Special Functions, May 1977
[11]	MacMahon, P.A.: Partitions of numbers whose graphs possess symmetry. Trans. Cambridge Phil. Soc.,17, 149-170 (1898-99)
[12]	MacMahon, P.A.: Combinatory Analysis, Vol. 2. London and New York: Cambridge University Press 1916 · JFM 46.0107.04
[13]	Muir, T.: A Treatise on the Theory of Determinants. London: Longmans 1933
[14]	Stanley, R.P.: Theory and applications of plane partitions I, Studies in Appl. Math.,50, 167-188 (1971) · Zbl 0225.05011
[15]	Stanley, R.P.: Theory and applications of plane partitions II, Studies in Appl. Math.50, 259-279 (1971) · Zbl 0225.05012
[16]	Whipple, F.J.W.: Well-poised series and other generalized hypergeometric series, Proc. London Math. Soc. (2),25, 525-544 (1926) · JFM 52.0365.03 · doi:10.1112/plms/s2-25.1.525
[17]	Whipple, F.J.W.: Some transformations of generalized hypergeometric series, Proc. London Math. Soc. (2),26, 257-272 (1927) · JFM 53.0331.03 · doi:10.1112/plms/s2-26.1.257
[18]	Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis, 4th ed., London and New York: Cambridge University Press 1958 · JFM 45.0433.02
[19]	Wilson, J.: Three-term contiguous relations and some new orthogonal polynomials, from Pade and Rational Approximation (Saff and Varga, eds.). New York-London: Academic Press, 1977
[20]	Wilson, J.: Ph.D. Thesis, University of Wisconsin, 1978