Order Quasisymmetric Functions Distinguish Rooted Trees

TL;DR

This paper proves that finite rooted trees can be uniquely identified by their order quasisymmetric functions, extending Stanley's conjecture from chromatic symmetric functions to posets.

Contribution

The paper establishes that order quasisymmetric functions distinguish finite rooted trees, providing a new tool for analyzing posets and extending previous conjectures.

Findings

Finite rooted trees are distinguishable by their order quasisymmetric functions.

The result extends Stanley's conjecture from chromatic symmetric functions to posets.

Provides a new method for identifying rooted trees in combinatorics.

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.