Young Tableaux in Combinatorics, Invariant Theory, and Algebra

Young Tableaux in Combinatorics, Invariant Theory, and Algebra: An Anthology of Recent Work is an anthology of papers on Young tableaux and their applications in combinatorics, invariant theory, and algebra. Topics covered include reverse plane partitions and tableau hook numbers; some partitions associated with a partially ordered set; frames and Baxter sequences; and Young diagrams and ideals of Pfaffians.

Comprised of 16 chapters, this book begins by describing a probabilistic proof of a formula for the number f? of standard Young tableaux of a given shape f?. The reader is then introduced to the generating function of R. P. Stanley for reverse plane partitions on a tableau shape; an analog of Schensted's algorithm relating permutations and triples consisting of two shifted Young tableaux and a set; and a variational problem for random Young tableaux. Subsequent chapters deal with certain aspects of Schensted's construction and the derivation of the Littlewood-Richardson rule for the multiplication of Schur functions using purely combinatorial methods; monotonicity and unimodality of the pattern inventory; and skew-symmetric invariant theory.

This volume will be helpful to students and practitioners of algebra.

Section 1: Combinatorics

1. A probabilistic Proof of a Formula for the Number of Young Tableaux of a Given Shape, Adv. Math. 31, 104-109 (1979)

2. Reverse Plane Partitions and Tableau Hook Numbers, J. Combinatorial Theory Ser. A. 21, 216-221 (1976)

3. An Analog of Schensted's Algorithm for Shifted Young Tableaux, J. Combinatorial Theory Ser. A 27, 10-18 (1979)

4. An Extension of Schensted's Theorem, Adv. Math. 14, 254-265 (1974)

5. Some Partitions Associated with a Partially Ordered Set, J. Combinatorial Theory Ser. A 20, 69-79 (1976)

6. A Variational Problem for Random Young Tableaux, Adv. Math. 26, 206-222 (1977)

7. On Schensted's Construction and the Multiplication of Schur Functions, Adv. Math. 30, 8-32 (1978)

8. Frames, Young Tableaux, and Baxter Sequences, Adv. Math. 26, 275-289 (1977)

9. Monotonicity and Unimodality of the Pattern Inventory, Adv. Math. 38, 101 - 1 0 8 (1980)

Section 2: Invariant Theory

10. Invariant Theory, Young Bitableaux, and Combinatorics, Adv. Math. 27, 63 - 92 (1978)

11. Skew-Symmetric Invariant Theory, Adv. Math. 21, 196-201 (1976)

12. A Characteristic Free Approach to Invariant Theory, Adv. Math. 21, 330-354 (1976)

Section 3: Algebra

13. Letter Place Algebras and a Characteristic-Free Approach to the Representation Theory of the General Linear and Symmetric Groups, I and II, Adv. Math. 33, 161-191 (1979); 38, 152-177 (1980)

14. Young Diagrams and Ideals of Pfaffians, Adv. Math. 35, 158-178 (1980)

15. On the Variety of Complexes, Adv. Math. 41, 57 - 77 (1981)

16. Syzygies des Variétés Déterminantales, Adv. Math. 30, 202-237 (1978)