Abstract. We compute the number of rhombus tilings of a hexagon with side lengths N;M;N;N;M;N, with N and M having the same parity, which contain a particular rhombus next to the center of the hexagon. The special case N = M of one of our results solves a problem posed by Propp. In the proofs, Hankel determinants featuring Bernoulli numbers play an important role.
|
174
|
Orthogonal Polynomials
– Szegö
- 1975
|
|
115
|
Generalized Hypergeometric Functions
– Slater
- 1966
|
|
115
|
The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
– Koekoek, Swarttouw
- 1998
|
|
113
|
A fast algorithm for proving terminating hypergeometric series identities
– Zeilberger
- 1990
|
|
109
|
The method of creative telescoping
– Zeilberger
- 1991
|
|
105
|
Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable
– Salvy, Zimmermann
- 1994
|
|
98
|
A Mathematica version of Zeilberger’s algorithm for proving binomial coefficient identities
– Paule, Schorn
- 1995
|
|
87
|
Combinatory Analysis
– MacMahon
- 1916
|
|
76
|
Analytic Theory of Continued Fractions
– WALL
- 1948
|
|
75
|
Higher transcendental functions
– Erdélyi, Magnus, et al.
- 1953
|
|
69
|
Nonintersecting paths, pfaffians, and plane partitions Adv
– Stembridge
- 1990
|
|
60
|
Theory of summation in finite terms
– Karr
- 1985
|
|
55
|
Discrete orthogonal polynomial ensembles and the Plancherel measure, Preprint (arXiv: math.CO/9906120
– Johansson
|
|
38
|
Enumeration of perfect matchings in graphs with reflective symmetry
– Ciucu
- 1997
|
|
34
|
unknown title
– Viennot
- 1983
|
|
32
|
Generating functions for plane partitions of a given shape
– Krattenthaler
- 1990
|
|
31
|
The problem of the calissons
– David, Tomei
- 1989
|
|
29
|
A Treatise on the Theory of Determinants
– Muir
- 1960
|
|
27
|
Advanced determinant calculus. Séminaire Lotharingien de Combinatoire B42q
– Krattenthaler
- 1999
|
|
27
|
Algorithmic manipulations and transformations of univariate holonomic functions and sequences
– Mallinger
- 1996
|
|
26
|
Bruhat lattices, plane partition generating functions, and minuscule representations
– Proctor
- 1984
|
|
25
|
Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions, Elect
– Krattenthaler
- 1997
|
|
25
|
Vorlesungen über Differenzenrechnung, Verlag von Julius
– Nörlund
- 1924
|
|
23
|
An alternative evaluation of the Andrews--Burge determinant
– Krattenthaler
- 1998
|
|
23
|
The Theory of Determinants in Historical Order of Development, (four volumes bound as two: Vol
– Muir
- 1960
|
|
18
|
Twenty open problems on enumeration of matchings, manuscript
– Propp
- 1996
|
|
18
|
The shape of a typical boxed plane partition
– Cohn, Larsen, et al.
- 1998
|
|
17
|
Some q-analogues of determinant identities which arose in plane partition enumeration
– Krattenthaler
- 1996
|
|
15
|
Symmetries of plane partitions and the permanent determinant method
– Kuperberg
- 1994
|
|
15
|
New symmetric plane partition identities from invariant theory work of DeConcini and
– Proctor
- 1990
|
|
14
|
Continued Fractions
– JONES, THRON
- 1980
|
|
13
|
The number of centered lozenge tilings of a symmetric hexagon
– Ciucu, Krattenthaler
- 1999
|
|
13
|
A determinant evaluation and some enumeration results for plane partitions
– Krattenthaler
- 1990
|
|
13
|
A new proof of the M--R--R conjecture --- including a generalization, preprint
– Krattenthaler
- 1999
|
|
13
|
Plane partitions I: A generalization of MacMahon's formula
– Ciucu
|
|
12
|
plane partitions, preprint
– Gessel, Viennot, et al.
- 1989
|
|
12
|
The Hahn and Meixner polynomials of an imaginary argument and some of their applications
– Atakishiyev, Suslov
- 1985
|
|
12
|
Enumeration of lozenge tilings of hexagons with a central triangular hole
– Ciucu, Eisenkölbl, et al.
|
|
10
|
Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten
– Krattenthaler, Zeilberger
- 1997
|
|
10
|
Vicious walkers and Young tableaux I: without walls
– Guttmann, Owczarek, et al.
- 1998
|
|
10
|
Shifted plane partitions of trapezoidal shape
– Proctor
- 1983
|
|
9
|
The story of 1,2,7,42,429,7436
– Robbins
- 1991
|
|
8
|
Continuous Hahn polynomials
– Askey
- 1985
|
|
8
|
Enumeration of lozenge tilings of hexagons with cut-off corners
– Ciucu, Krattenthaler
|
|
8
|
An exploration of the permanent-determinant method, Electron
– Kuperberg
- 1998
|
|
8
|
The number of rhombus tilings of a "punctured" hexagon and the minor summation formula
– Okada, Krattenthaler
- 1998
|
|
6
|
Enumeration of matchings: Problems and progress, in: "New Perspectives in Geometric Combinatorics
– Propp
- 1999
|
|
5
|
Exact enumeration of certain tilings of diamonds and hexagons with defects, preprint
– Helfgott, Gessel
- 1999
|
|
5
|
Four symmetry classes of plane partitions under one roof
– Kuperberg
- 1996
|
|
4
|
Matrix theory, Editions de Physique
– Mehta
- 1989
|
|
