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

MSC:
11P81Elementary theory of partitions
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)
[3]Andrews, G.E.: The Theory of Partitions, Addision-Wesley, Reading, 1976
[4]Andrews, G.E.: Plane partitions (I): the MacMahon conjecture, Advances in Math. (to appear)
[5]Andrews, G.E.: On Macdonald’s conjecture and descending plane partitions, Proceedings of the Alfred Young Day Conference (to appear)
[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)
[7]Bailey, W.N.: Generalized Hypergeometric Series. London and New York: Cambridge University Press 1935
[8]Carlitz, L.: Rectangular arrays and plane partitions, Acta Arith.,13, 22-47 (1967)
[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
[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)
[15]Stanley, R.P.: Theory and applications of plane partitions II, Studies in Appl. Math.50, 259-279 (1971)
[16]Whipple, F.J.W.: Well-poised series and other generalized hypergeometric series, Proc. London Math. Soc. (2),25, 525-544 (1926) · 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) · 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
[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