# 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Determinants, paths, and plane partitions, unpublished manuscript.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.