(-1)-Enumeration of plane partitions with complementation symmetry

Advances in Applied Mathematics

Volumn 30, Issue 1-2, 2003, Pages 53-95

  Eisenkölbl, Theresia ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Determinants; Lozenge tilings; Nonintersecting lattice paths; Pfaffians; Plane partitions; Rhombus tilings

Indexed keywords

EID: 0038742979     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0196-8858(02)00525-0     Document Type: Review

References (26)

1. G.E. Andrews, Plane partitions (II): The equivalence of the Bender-Knuth and the MacMahon conjectures, Pacific J. Math. 72 (1977) 283-291.
2. G.E. Andrews, Plane partitions (I): The MacMahon conjecture, Adv. Math. Suppl. Stud. 1 (1978) 131-150.
3. G.E. Andrews, Plane partitions V: The t.s.s.c.p.p. conjecture, J. Combin. Theory Ser. A 66 (1994) 28-39.
4. I.M. Gessel, X. Viennot, Determinant, paths and plane partitions, Preprint, 1989.
5. R.W. Gosper, Decision procedure for indefinite hypergeometric summation, Proc. Natl. Acad. Sci. USA 75 (1978) 40-42.
6. M. Ishikawa, M. Wakayama, Minor summation formula of Pfaffians, Linear and Multilinear Algebra 39 (1995) 285-305.
7. C. Krattenthaler, Generating functions for plane partitions of a given shape, Manuscripta Math. 69 (1990) 173-202.
8. G. Kuperberg, An exploration of the permanent-determinant method, Electron. J. Combin. 5 (1998) #R46, math.CO/9810091.
9. G. Kuperberg, Symmetries of plane partitions and the permanent determinant method, J. Combin. Theory Ser. A 68 (1994) 115-151.
10. G. Kuperberg, Private communication, November 22, 2000.
11. B. Lindström, On the vector representations of induced matroids, Bull. London Math. Soc. 5 (1973) 85-90.
12. P.A. MacMahon, Combinatory Analysis, Vol. 2 Cambridge Univ. Press, 1916, reprinted by Chelsea, New York, 1960.
13. Mills, Robbins, Rumsey, Enumeration of a symmetry class of plane partitions, Discrete Math. 67 (1987) 43-55.
14. W.H. Mills, D.H. Robbins, H. Rumsey, Proof of the Macdonald conjecture, Invent. Math. 66 (1982) 73-87.
15. S. Okada, On the generating functions for certain classes of plane partitions, J. Combin. Theory Ser. A 51 (1989) 1-23.
16. S. Okada, Applications of minor summation formulas to rectangular-shaped representations of classical groups, J. Algebra 205 (1998) 337-367.
17. L.J. Slater, Generalized hypergeometric functions, Cambridge Univ. Press, Cambridge, 1966.
18. R.P. Stanley, Enumerative Combinatorics, Vol. 1, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1986.
19. R.P. Stanley, Symmetries of plane partitions, J. Combin. Theory Ser. A 43 (1986) 103-113; Erratum: J. Combin. Theory Ser. A 44 (1987) 310.
20. J.R. Stembridge, Nonintersecting paths, Pfaffians and plane partitions, Adv. Math. 83 (1990) 96-131.
21. J.R. Stembridge, Some hidden relations involving the ten symmetry classes of plane partitions, J. Combin. Theory Ser. A 68 (1994) 372-409.
22. J.R. Stembridge, On minuscule representations, plane partitions and involutions in complex Lie groups, Duke Math. J. 73 (1994) 469-490.
23. J.R. Stembridge, The enumeration of totally symmetric plane partitions, Adv. Math. 111 (1995) 227-245.
24. D. Zeilberger, The method of creative telescoping, J. Symbolic Comput. 11 (1991) 195-204.
25. D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990) 207-211.
26. D. Zeilberger, Proof of the alternating sign matrix conjecture, Electron. J. Combin. 3 (2) (1996), The Foata Festschrift Res. Paper #R13, 84 p., math.CO/9407211.