2014/09/17 by Ricky Ini Liu, Liu, Ricky Ini
Mathematics · #05E15 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E15
paper · pdf · doi:10.48550/arxiv.1409.4872
11 pages, 3 figures
arxiv created 2014/09/17 · openalex publication_date 2014/09/17 · arxiv updated 2014/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Fomin-Kirillov algebra \mathcal En is a noncommutative algebra with a generator for each edge in the complete graph on n vertices. For any graph G on n vertices, let \mathcal EG be the subalgebra of \mathcal En generated by the edges in G. We show that the commutative quotient of \mathcal EG is isomorphic to the Orlik-Terao algebra of G. As a consequence, the Hilbert series of this quotient is given by (-t)n χG(-t-1), where χG is the chromatic polynomial of G. We also give a reduction algorithm for the graded components of \mathcal EG that do not vanish in the commutative quotient and show that their structure is described by the combinatorics of noncrossing forests.