Table of Contents
1. Reduced Factorizations..................................................5
1.1 Notation......................................................................5
1.2 The Matrix Approach........................................................12
2. Balanced Labelled Circle Diagrams..................................25
2.1 From Matrices to Tabloids....................................................25
2.2 Descents and Kevin Kadel’s ZIGZAGs .......................................33
2.3 Special Circle Diagrams......................................................37
2.4 The Lascoux-Schutzenberger Tree of a General Permutation ..................48
3. Symmetric Functions and Schubert Polynomials..................65
3.1 Stanley’sTheory of P-Partitions..............................................65
3.2 The Stanley Symmetric function of a Permutation ............................72
3.3 Divided Differences and Schubert Polynomials ..............................85
Appendix by David Little
4. A Combinatorial refinementof the Lascoux-Schutzenberger Tree..............103
4.1 The bijection. ...............................................................103
4.2 The Applet..................................................................107
4.3 The Schensted and Edelman-Greene correspondences as particular cases.....109
References.................................................................113
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