Abstract
We compute the number of rhombus tilings of a hexagon with sidesN,M,N, N,M,N, which contain a fixed rhombus on the symmetry axis that cuts through the sides of lengthM.
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References
M. Ciucu, Enumeration of perfect matchings in graphs with reflective symmetry, J. Combin. Theory Ser. A77 (1997) 67–97.
M. Ciucu and C. Krattenthaler, The number of centered lozenge tilings of a symmetric hexagon, J. Combin. Theory Ser. A, to appear.
H. Cohn, M. Larsen, and J. Propp, The shape of a typical boxed plane partition, preprint.
G. David and C. Tomei, The problem of the calissons, Amer. Math. Monthly96 (1989) 429–431.
M. Fulmek and C. Krattenthaler, The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II, in preparation.
I. M. Gessel and X. Viennot, Determinants, paths, and plane partitions, preprint, 1989.
H. Helfgott and I. M. Gessel, Exact enumeration of certain tilings of diamonds and hexagons with defects, preprint.
C. Krattenthaler, Generating functions for plane partitions of a given shape, Manuscripta Math.69 (1990) 173–202.
C. Krattenthaler, A determinant evaluation and some enumeration results for plane partitions, In: Number-Theoretic Analysis, E. Hlawka and R. F. Tichy, Eds., Lect. Notes in Math., Vol. 1452, Springer-Verlag, Berlin, 1990.
C. Krattenthaler, Someq-analogues of determinant identities which arose in plane partition enumeration, Séminaire Lotharingien Combin.36 (1996) paper B36e, 23 pp.
C. Krattenthaler, A new proof of the M-R-R conjecture—including a generalization, J. Difference Equation Appl., to appear.
C. Krattenthaler, An alternative evaluation of the Andrews—Burge determinant, In: Mathematical Essays in Honor of Gian-Carlo Rota, B. E. Sagan and R. P. Stanley, Eds., Progress in Math., Vol. 161, Birkhäuser, Boston, 1998, pp. 263–270.
C. Krattenthaler, Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions, Electron. J. Combin.4(1) (1997) #R27, 62 pp.
C. Krattenthaler and D. Zeilberger, Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten, New York J. Math.3 (1997) 54–102.
P.A. MacMahon, Combinatory Analysis, Vol. 2, Cambridge University Press, 1916; reprinted by Chelsea, New York, 1960.
J. Propp, Twenty open problems on enumeration of matchings, manuscript, 1996.
A.P. Prudnikov, Yu.A. Brychkov, and O.I. Marichev, Integrals and Series, Vol. 3: More Special Functions, Gordon and Breach, New York, London, 1989.
L. J. Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.
J. R. Stembridge, Nonintersecting paths, pfaffians and plane partitions, Adv. in Math.83 (1990) 96–131.
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Fulmek, M., Krattenthaler, C. The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, I. Annals of Combinatorics 2, 19–41 (1998). https://doi.org/10.1007/BF01626027
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DOI: https://doi.org/10.1007/BF01626027