Author(s): Anders Skovsted Buch
Series: PhD thesis at University of Chicago
Year: 1999
ABSTRACT ii
ACKNOWLEDGEMENTS iv
LIST OF FIGURES vi
1 INTRODUCTION 1
1.1 Degeneracy lo c i ................................................................................................ 1
1.2 Description of the algorithm ......................................................................... 3
1.3 A conjecture for the coefficients c „ ( r) ........................................................ 6
2 RESULTS ABOUT THE CONJECTURED FORMULA 9
2.1 Paths through the rank diagram .................................................................. 9
2.2 A criterion for factor sequences .................................................................. 12
2.3 An involution of Fom in ................................................................................... 19
2.4 The stronger conjecture ................................................................................ 24
2.5 Proof in a special c a s e ................................................................................... 27
3 STANLEY SYMMETRIC FUNCTIONS 31
3.1 Introduction ....................................................................................................... 31
3.2 Schubert polynomials ...................................................................................... 33
3.3 Stable Schubert polynomials ......................................................................... 35
3.4 Redundant rank conditions and products of perm utations ................... 39
3.5 Relations to a conjectured Littlewood-Richardson rule .......................... 42
REFERENCES 46
