#### Date of Thesis

2011

#### Thesis Type

Honors Thesis

#### Department

Mathematics

#### First Advisor

Peter McNamara

#### Keywords

quasisymmetric functions, P-partitions, generating functions, posets

#### Abstract

To every partially ordered set (poset), one can associate a generating function, known as the P-partition generating function. We find necessary conditions and sufficient conditions for two posets to have the same P-partition generating function. We define the notion of a jump sequence for a labeled poset and show that having equal jumpsequences is a necessary condition for generating function equality. We also develop multiple ways of modifying posets that preserve generating function equality. Finally, we are able to give a complete classification of equalities among partially ordered setswith exactly two linear extensions.

#### Recommended Citation

Ward, Ryan, "Equality of P-partition Generating Functions" (2011). *Honors Theses*. 10.

http://digitalcommons.bucknell.edu/honors_theses/10

## Comments

PUBLIC