A non-automatic (!) application of gosper’s algorithm evaluates a determinant from tiling enumeration

Rocky Mountain Journal of Mathematics

Volumn 32, Issue 2, 2002, Pages 589-605

  Ciucu, M ^a   Krattenthaler, C ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Determinant evaluations; Gosper s algorithm; Hypergeometric series; Lozenge tilings; Nonintersecting lattice paths; Plane partitions; Rhombus tilings

Indexed keywords

EID: 0036624875     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1030539688     Document Type: Article

References (23)

1. G.E.Andrews and W.H. Burge, Determinant identities, PacificJ. Math158(1993), 1-14.
2. M.Ciucu, T.Eisenkolbl, C.Krattenthaler and D. Zare, Enumeration of lozenge tilings of hexagons with a central triangular hole, J. Combin. Theory Ser. A. 95(2001), 251-334.
3. M.Ciucu and C. Krattenthaler, The number of centered lozenge tilings of a symmetric hexagon, J. Combin. Theory Ser. A. 86(1999), 103-126.
4. M. Ciucu and C. Krattenthaler, Enumeration of lozenge tilings of hexagons with cut off corners, J. Combin. Theory Ser.A (to appear).
5. T. Eisenkolbl, Rhombus tilings of a hexagon with two triangles missing on the symmetry axis, Electr. J. Combin. 6(1) (1999), #R30.
6. M.Fulmek and C. Krattenthaler, The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, I, Ann. Combin. 2(1998), 19-40.
7. M.Fulmek and C. Krattenthaler, The number of rhombus tilings of a symmetric hexagon which contain a fixed rhombus on the symmetry axis, II, Europ. J. Combin. 21(2000), 601-640.
8. I.M.Gessel and X. Viennot, Binomial determinants, paths, and hook length formulae, Adv. Math. 58(1985), 300-321.
9. R.W. Gosper, Decision procedure for indefinite hypergeometric summation, Proc. Natl. Acad. Sci. USA75(1978), 40-42.
10. R.L.Graham, D. E.Knuth and O.Patashnik, Concrete mathematics, Addison-Wesley, Reading, Massachusetts, 1989.
11. C. Krattenthaler, Some q-analogues of determinant identities which arose in plane partition enumeration, Seminaire Lotharingien Combin. 36 (1996), Art.B36e, 23 pages.
12. C. Krattenthaler, Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions, Elect. J. Combin. 4(1) (1997), #R27.
13. C. Krattenthaler, An alternative evaluation of the Andrews-Burge determinant, in Mathematical essays in honor of Gian-Carlo Rota, B.E. Sagan and R.P. Stanley, eds., Birkhauser, Boston, 1998, 263-270.
14. C. Krattenthaler, A new proof of the M-R-R conjecture-including a generalization, J. Difference Eq. Appl. 5(1999), 335-351.
15. C. Krattenthaler, Advanced determinant calculus, Seminaire Lotharingien Combin. 42 (1999), Art.B42q, 66 pages.
16. C.Krattenthaler and D. Zeilberger, Proof of a determinant evaluation conjectured by Bombieri, Hunt and van der Poorten, New YorkJ. Math. 3(1997), 54-102.
17. G. Kuperberg, Another proof of the alternating sign matrix conjecture, Int. Math. Res. Notices3, (1996), 139-150.
18. B. Lindstrom, On the vector representations of induced matroids, Bull. London Math. Soc. 5(1973), 85-90.
19. M. Petkovsek and H. S. Wilf, When can the sum of (1/p)th of the binomial coefficients have closed form?, Electron. J. Combin. 4(2) (1997), #R21,7 pages.
20. M. Petkovsek, H. Wilf and D. Zeilberger, A= B, A.K. Peters, Wellesley, 1996.
21. A.J. van der Poorten, A powerful determinant, Experimental Math. 10 (2001), 307-320.
22. L.J.Slater, Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.
23. J.R. Stembridge, Nonintersecting paths, pfaffians and plane partitions, Adv. Math. 83(1990), 96-131.