Symmetry classes of alternating-sign matrices under one roof

Annals of Mathematics

Volumn 156, Issue 3, 2002, Pages 835-866

  Kuperberg, Greg ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036880530     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/3597283     Document Type: Article

References (38)

1. D. M. BRESSOUD, Proofs and Confirmations, Mathematical Association of America, Washington, DC, 1999.
2. D. M. BRESSOUD and J. PROPP, How the alternating sign matrix conjecture was solved, Notices Amer. Math. Soc. 46 (1999), 637-646.
3. I. CHEREDNIK, Factorizing particles on a half line, and root systems, Teoret. Mat. Fiz. 61 (1984), 35-44.
4. M. CIUCU, Perfect matchings of cellular graphs, J. Algebraic Combin. 5 (1996), 87-103.
5. _, Enumeration of perfect matchings in graphs with reflective symmetry, J. Combin. Theory Ser. A 77 (1997), 67-97.
6. H. COHN and J. PROPP, private communication.
7. H. J. DE VEGA and A. GONZÁLEZ-RUIZ, Boundary K-matrices for the XYZ, XXZ and XXX spin chains, J. Phys. A 27 (1994), 6129-6137 (arXiv:hep-th/9306089).
8. V. DRINFEL'd, Quantum groups, Proc. Internat. Congress of Mathematicians (Berkeley, California) 1 (1986), 798-820.
9. N. ELKIES, G. KUPERBERG, M. LARSEN, and J. PROPP, Alternating-sign matrices and domino tilings, I, J. Algebraic Combin. 1 (1992), 111-132.
10. _, Alternating-sign matrices and domino tilings, II, J. Algebraic Combin. 1 (1992), 219-234.
11. I. J. GOOD, Short proof of a conjecture by Dyson, J. Mathematical Phys. 11 (1970), 1884.
12. A. G. IZERGIN, Partition function of a six-vertex model in a finite volume, Dokl. Akad. Nauk SSSR 297 (1987), 331-333.
13. A. G. IZERGIN, D. A. COKER, and V. E. KOREPIN, Determinant formula for the six-vertex model, J. Phys. A 25 (1992), 4315-4334.
14. W. JOCKUSCH, Perfect matchings and perfect squares, J. Combin. Theory Ser. A 67 (1994), 100-115.
15. W. JOCKUSCH and J. PROPP, Antisymmetric monotone triangles and domino tilings of quartered Aztec diamonds, preprint.
16. D. E. KNUTH, Overlapping Pfaffians, Electron. J. Combin. 3 (1996), #R5.
17. V. KOREPIN and P. ZINN-JUSTIN, Thermodynamic limit of the six-vertex model with domain wall boundary conditions, J. Phys. A. 33 (2000), 7053-7066 (arXiv:cond-mat/0004250).
18. V. E. KOREPIN, Calculation of norms of Bethe wave functions, Comm. Math. Phys. 86 (1982), 391-418.
19. V. E. KOREPIN, N. M. BOGOLIUBOV, and A. G. IZERGIN, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Univ. Press, Cambridge, England, 1993.
20. C. KRATTENTHALER, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 (1999), B42q (arXiv:math.CO/9902004).
21. n(n+1)/2, http://www.math.wisc.edu/̃propp/reading.html.
22. G. KUPERBERG, Another proof of the alternating sign matrix conjecture, Internat. Math. Res. Notices 1996 (1996), 139-150 (arXiv:math.CO/9712207).
23. D. LAKSOV, A. LASCOUX, and A. THORUP, On Giambelli's theorem on complete correlations, Acta Math. 162 (1989), 143-199.
24. E. H. LIEB, Exact solution of the problem of the entropy of two-dimensional ice, Phys. Rev. Lett. 18 (1967), 692-694.
25. Maple, http://www.maplesoft.com/.
26. W. H. MILLS, D. P. ROBBINS, and H. RUMSEY, Alternating sign matrices and descending plane partitions, J. Combin. Theory Ser. A 34 (1983), 340-359.
27. J. PROPP, Memo on urban renewal, http://www.math.wisc.edu/̃propp/reading.html.
28. PSTricks, http://www.tug.org/applications/PSTricks/.
29. REVTeX 4, http://publish.aps.org/revtex4/.
30. D. P. ROBBINS, Symmetry classes of alternating sign matrices (arXiv:math.CO/0008045).
31. D. P. ROBBINS, The story of 1,2,7,42,429,7436,..., Math. Intelligencer 13 (1991), 12-19.
32. D. P. ROBBINS and H. RUMSEY, Determinants and alternating sign matrices, Adv. in Math. 62 (1986), 169-184.
33. E. K. SKLYANIN, Boundary conditions for integrable quantum systems, J. Phys. A 21 (1988), 2375-2389.
34. K. SOGO, Time-dependent orthogonal polynomials and theory of soliton. Applications to matrix model, vertex model and level statistics, J. Phys. Soc. Japan 62 (1993), 1887-1894.
35. J. R. STEMBRIDGE, Nonintersecting paths, Pfaffians, and plane partitions, Adv. in Math. 83 (1990), 96-131.
36. T. SUNDQUIST, Two variable Pfaffian identities and symmetric functions, J. Algebraic Combin. 5 (1996), 135-148.
37. O. TSUCHIYA, Determinant formula for the six-vertex model with reflecting end, J. Math. Phys. 39 (1998), 5946-5951 (arXiv:solv-int/9804010).
38. D. ZEILBERGER, Proof of the alternating sign matrix conjecture, Elec. J. Comb. 3 (1996) (arXiv:math.CO/9407211).