Order Quasisymmetric Functions Distinguish Rooted Trees

Abstract

Richard P. Stanley conjectured that finite trees can be distinguished by their chromatic symmetric functions. In this paper, we prove an analogous statement for posets: Finite rooted trees can be distinguished by their order quasisymmetric functions.

16 pages, 5 figures, referees' suggestions incorporated

References in corpus (2)

• A historical survey of P-partitions
• Symmetric Chromatic Polynomial of Trees

Cited by in corpus (7)

• The Chromatic Symmetric Functions of Trivially Perfect Graphs and Cographs
• $P$-partitions and $p$-positivity
• Quasisymmetric functions distinguishing trees
• Positivity among P-partition generating functions
• Reconstructing Rooted Trees From Their Strict Order Quasisymmetric Functions
• $P$-Partitions and Quasisymmetric Power Sums
• On the smallest trees with the same restricted $U$-polynomial and the rooted $U$-polynomial