Enumeration of Rhombus Tilings of a Hexagon which Contain a Fixed Rhombus in the Centre

We compute the number of rhombus tilings of a hexagon with side lengths a, b, c, a, b, c which contain the central rhombus and the number of rhombus tilings of a hexagon with side lengths a, b, c, a, b, c which contain the “almost central” rhombus above the centre.

[1]  Christian Krattenthaler,et al.  The Number of Rhombus Tilings of a Symmetric Hexagon which Contain a Fixed Rhombus on the Symmetry Axis, II , 2000, Eur. J. Comb..

[2]  W. J. Thron,et al.  Encyclopedia of Mathematics and its Applications. , 1982 .

[3]  Carlos Tomei,et al.  The Problem of the Calissons , 1989 .

[4]  R. W. Gosper.  Decision procedure for indefinite hypergeometric summation. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[5]  J. Shaw.  Combinatory Analysis , 1917, Nature.

[6]  Christian Krattenthaler,et al.  HYP and HYPQ Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively q-binomial sums and basic hypergeometric series , 1993 .

[7]  Christian Krattenthaler,et al.  HYP and HYPQ , 1995, J. Symb. Comput..

[8]  B. Lindström.  On the Vector Representations of Induced Matroids , 1973 .

[9]  Lucy Joan Slater,et al.  Generalized hypergeometric functions , 1966 .

[10]  Michael Larsen,et al.  The Shape of a Typical Boxed Plane Partition , 1998, math/9801059.

[11]  Mizan Rahman,et al.  Basic Hypergeometric Series , 1990 .

[12]  T. Koornwinder,et al.  BASIC HYPERGEOMETRIC SERIES (Encyclopedia of Mathematics and its Applications) , 1991 .

[13]  Mihai Ciucu,et al.  The Number of Centered Lozenge Tilings of a Symmetric Hexagon , 1999, J. Comb. Theory, Ser. A.

[14]  G. Rw.  Decision procedure for indefinite hypergeometric summation , 1978 .

[15]  C. Krattenthaler.  ADVANCED DETERMINANT CALCULUS , 1999, math/9902004.

[16]  Peter Paule,et al.  A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities , 1995, J. Symb. Comput..