Lecture materials for "Tilings and Plane Partitions"


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Ira M. Gessel and X. G. Viennot, Determinants, paths, and plane partitions, unpublished manuscript.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.



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.