Lecture materials for "Tilings and Plane Partitions"
Literature
David M. Bressoud. Proofs and confirmations.
The story of the alternating sign matrix conjecture.
MAA Spectrum. Mathematical Association of America, Washington, DC;
Cambridge University Press, Cambridge, 1999. xvi+274 pp.
Plane Partitions and Non-Intersecting Lattice Paths
Bernt Lindström, On the vector representations of induced matroids.
Bull. London Math. Soc. 5 (1973), 85--90.
Ira M. Gessel and X. G. Viennot,
Determinants, paths, and plane partitions, unpublished manuscript.
Plane Partitions and Pfaffians
Soichi Okada, On the generating functions for certain classes of
plane partitions. J. Combin. Theory Ser. A 51 (1989), no. 1, 1-23.
John R. Stembridge, Nonintersecting paths, Pfaffians, and plane partitions.
Adv. Math. 83 (1990), no. 1, 96--131.
Minor Summation Formula
Masao Ishikawa
and Masato Wakayama, Minor summation formula of Pfaffians.
Linear and Multilinear Algebra 39 (1995), no. 3, 285-305.
Determinant Evaluations
Christian Krattenthaler,
Advanced determinant calculus. Séminaire Lotharingien Combin. 42
("The Andrews Festschrift") (1999), Article B42q, 67 pp.
Christian Krattenthaler,
Advanced determinant calculus: a complement.
Linear Algebra Appl. 411 (2005), 68-166.
Symmetric Functions
Ian G. Macdonald, Symmetric functions and Hall polynomials.
Second edition. With contributions by A. Zelevinsky. Oxford Mathematical Monographs.
Oxford Science Publications. The Clarendon Press, Oxford University Press,
New York, 1995. x+475 pp.
Alain Lascoux, Symmetric functions and combinatorial operators on polynomials.
CBMS Regional Conference Series in Mathematics, 99. Published for the
Conference Board of the Mathematical Sciences, Washington, DC; by the
American Mathematical Society, Providence, RI, 2003. xii+268 pp.
Richard P. Stanley, Enumerative combinatorics. Vol. 2. With a foreword by
Gian-Carlo Rota and appendix 1 by Sergey Fomin. Cambridge Studies in Advanced
Mathematics, 62. Cambridge University Press, Cambridge, 1999. xii+581 pp.
(Chapter 7)
Algorithmic Summation
Marko Petkovsek, Herbert Wilf and Doron Zeilberger,
A=B. With a foreword by Donald E. Knuth.
With a separately available computer disk. A K Peters, Ltd., Wellesley,
MA, 1996. xii+212 pp.
Guessing
Rate
Guess
(Martin Rubey)
gfun
(Bruno Salvy)
Guess.m
(Manuel Kauers)
What do alternating sign matrices have to do with totally symmetric
self-complementary plane partitions?
Christian Krattenthaler,
A gog-magog conjecture. Manuscript, 1996.