Abstract
We give a short, self-contained evaluation of the Andrews-Burge determinant (Pacific J. Math. 158 (1994), 1–14).
Supported in part by EC’s Human Capital and Mobility Program, grant CHRX-CT93-0400 and the Austrian Science Foundation FWF, grant P10191-MAT
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. E. Andrews, Plane partitions (II): The equivalence of the Bender-Knuth and the MacMahon conjectures, Pacific J. Math. 72 (1977), 283–291.
G. E. Andrews, Plane partitions (I): The MacMahon conjecture, in: Studies in Foundations and Combinatorics, G.-C. Rota (ed.), Adv. in Math. Suppl. Studies, Vol. 1, 1978, 131–150.
G. E. Andrews, Plane partitions (III): The weak Macdonald conjecture, Inventiones Math. 53 (1979), 193–225.
G. E. Andrews, Macdonald’s conjecture and descending plane partitions, in: Combinatorics, representation theory and statistical methods in groups, Young Day Proceedings, T. V. Narayana, R. M. Mathsen, J. G. Williams (eds.), Lecture Notes in Pure Math., vol. 57, Marcel Dekker, New York, Basel, 1980,91–106.
G. E. Andrews, Plane partitions (IV): A conjecture of Mills-Robbins-Rumsey, Aequationes Math. 33 (1987), 230–250.
G. E. Andrews, Plane partitions V: The t.s.s.c.p.p. conjecture, J. Combin. Theory Ser. A 66 (1994), 28–39.
G. E. Andrews, Pfaff’s method (I): The Mills-Robbins-Rumsey determinant, preprint.
G. E. Andrews and D. W. Stanton, Determinants in plane partition enumeration, preprint.
G. E. Andrews and W. H. Burge, Determinant identities, Pacific J. Math. 158 (1993), 1–14.
I. P. Goulden and D. M. Jackson, Further determinants with the averaging property of Andrews-Burge, J. Combin. Theory Ser. A 73 (1996), 368–375.
C. Krattenthaler, Determinant identities and a generalization of the number of totally symmetric self-complementary plane partitions, Elect. J. Combin. (to appear).
C. Krattenthaler, Some q-analogues of determinant identities which arose in plane partition enumeration, Séminaire Lotharingien Combin. (to appear).
C. Krattenthaler, A new proof of the MRR-conjecture — including a generalization, preprint.
G. Kuperberg, Another proof of the alternating sign matrix conjecture, Math. Research Letters (1996), 139–150.
W. H. Mills, D. H. Robbins and H. Rumsey, Enumeration of a symmetry class of plane partitions, Discrete Math. 67 (1987), 43–55.
M. Petkovšek and H. Wilf, A high-tech proof of the Mills-Robbins-Rumsey determinant formula, Elect. J. Combin. 3 (no. 2, “The FoataFestschrift”) (1996), #R19, 3 pp.
B. Salvy and P. Zimmermann, GFUN — A MAPLE package for the manipulation of generating and holonomic functions in one variable, ACM Trans. Math. Software 20 (1994), 163–177.
D. Zeilberger, A fast algorithm for proving terminating hypergeometric identities, Discrete Math. 80 (1990), 207–211.
D. Zeilberger, The method of creative telescoping, J. Symbolic Comput. 11 (1991), 195–204.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Birkhäuser
About this chapter
Cite this chapter
Krattenthaler, C. (1998). An Alternative Evaluation of the Andrews-Burge Determinant. In: Sagan, B.E., Stanley, R.P. (eds) Mathematical Essays in honor of Gian-Carlo Rota. Progress in Mathematics, vol 161. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4108-9_13
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4108-9_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8656-1
Online ISBN: 978-1-4612-4108-9
eBook Packages: Springer Book Archive