The Number of Rhombus Tilings of a "Punctured" Hexagon and the Minor Summation Formula

Advances in Applied Mathematics

Volumn 21, Issue 3, 1998, Pages 381-404

  Okada, S ^a   Krattenthaler, C ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Rhombus tilings; lozenge tilings; plane partitions; nonintersecting lattice paths; Schur functions

Indexed keywords

EID: 0040599034     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1998.0602     Document Type: Article

References (14)

1. Ciucu M. Enumeration of perfect matchings in graphs with reflective symmetry. J. Combin. Theory Ser. A. 77:1997;67-97.
2. Fulmek M., Krattenthaler C. Lattice path proofs for determinant formulas for symplectic and orthogonal characters. J. Combin. Theory Ser. A. 77:1997;3-50.
3. I. M. Gessel, X. Viennot, Determinants, paths, and plane partitions, 1989.
4. Ishikawa M., Wakayama M. Minor summation formula for pfaffians. Linear and Multilinear Algebra. 39:1995;285-305.
5. Ishikawa M., Wakayama M. Minor summation formula of pfaffians and Schur function identities. Proc. Japan Acad. Ser. A. 71:1995;54-57.
6. Ishikawa M., Okada S., Wakayama M. Applications of minor summation formulas I, Littlewood's formulas. J. Algebra. 183:1996;193-216.
7. Kuperberg G. Symmetries of plane partitions and the permanent determinant method. J. Combin. Theory Ser. A. 68:1994;115-151.
8. Macdonald I. G. Symmetric Functions and Hall Polynomials. 1995;Oxford Univ. Press, New York/London.
9. MacMahon P. A. Combinatory Analysis. 1916;Cambridge Univ. Press.
10. S. Okada, Applications of minor summation formulas to rectangular-shaped representations of classical groups, J. Algebra.
11. f1.
12. Sagan B. E. The Symmetric Group. 1991;Wadsworth & Brooks/Cole, Pacific Grove.
13. Stembridge J. R. Nonintersecting paths, pfaffians and plane partitions. Adv. in Math. 83:1990;96-131.
14. M. Ciucu, Enumeration of Lozenge tilings of punctured hexagons, J. Combin. Theory Ser. A.