Quasisymmetric functions distinguishing trees

Abstract

A famous conjecture of Stanley states that his chromatic symmetric function distinguishes trees. As a quasisymmetric analogue, we conjecture that the chromatic quasisymmetric function of Shareshian and Wachs and of Ellzey distinguishes directed trees. This latter conjecture would be implied by an affirmative answer to a question of Hasebe and Tsujie about the $P$-partition enumerator distinguishing posets whose Hasse diagrams are trees. They proved the case of rooted trees and our results include a generalization of their result.

22 pages, 11 figures. To appear in Algebraic Combinatorics

References in corpus (2)

• Symmetric Chromatic Polynomial of Trees
• Reconstructing Rooted Trees From Their Strict Order Quasisymmetric Functions

Cited by in corpus (1)

• Equivalence classes of lower and upper descent weak Bruhat intervals