Author(s): David D. Gebhard
Series: PhD Thesis
Publisher: Michigan State University
Year: 1998
IN T R O D U C T IO N 1
1 P relim inaries 7
1 . 1 Symmetric F unctions ........................................................................................... 7
1.2 The Chromatic Symmetric Function. A 'c ..................................................... 10
2 T he N oncom m utative C ase 15
2 . 1 Symmetric Functions in Noncommuting V ariab les ................................... 15
2.2 Development and Results for Y q ................................................................... 20
3 O rientations and Sinks 29
3.1 Acyclic Orientations ........................................................................................... 29
3.2 The Modified Blass-Sagan A lgorithm ............................................................ 34
4 R esults on e-positivity 41
4.1 Inducing e „ ............................................................................................................ 41
4.2 Some e-positivity R esults .................................................................................... 48
4.3 The (3-F1 )-free C onjecture ................................................................................ 56
5 O pen P roblem s and C onjectures 67
5.1 Partitioning Acyclic O rien tatio n s .................................................................. 67
5.2 A' g and T re e s ......................................................................................................... 70
B IB L IO G R A P H Y 74
