2013/06/10 by Mathieu Guay-Paquet, Guay-Paquet, Mathieu · 5 citations
Computer Science · Mathematics · #06A07 (Primary) 05E05 (Secondary) #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1306.2400
openalex publication_date 2013/06/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider a linear relation which expresses Stanley's chromatic symmetric\nfunction for a poset in terms of the chromatic symmetric functions of some\nclosely related posets, which we call the modular law. By applying this in the\ncontext of (3+1)-free posets, we are able to reduce Stanley and Stembridge's\nconjecture that the chromatic symmetric functions of all (3+1)-free posets are≠-positive to the case of (3+1)-and-(2+2)-free posets, also known as unit\ninterval orders. In fact, our reduction can be pushed further to a much smaller\nclass of posets, for which we have no satisfying characterization. We also\nobtain a new proof of the fact that all 3-free posets have e-positive chromatic\nsymmetric functions.\n