Séminaire Lotharingien de Combinatoire, 93B.31 (2025), 12 pp.
Tatsuyuki Hikita
On the Stanley-Stembridge Conjecture
Abstract.
The Stanley-Stembridge conjecture was a long-standing problem in algebraic combinatorics which states that the chromatic symmetric function for any (3+1)-free graph expands positively in terms of elementary symmetric functions. We explain how to find an inductive and positive formula for the elementary symmetric function expansion of chromatic quasisymmetric function for any unit interval graph, which in particular implies the Stanley-Stembridge conjecture.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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