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The operads of planar forests are Koszul

2009/03/09 by Loïc Foissy, Foissy, Loïc
Computer Science · Engineering · Mathematics · #05C05 #18D50 #FOS: Mathematics #Polynomial and algebraic computation #Rings and Algebras (math.RA) #Slime Mold and Myxomycetes Research #Topological and Geometric Data Analysis #math.RA #msc:05C05 #msc:18D50

paper · pdf · doi:10.48550/arxiv.0903.1554

18 pages

arxiv created 2009/03/09 · openalex publication_date 2009/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the Koszul dual of two quadratic operads on planar forests introduced to study the infinitesimal Hopf algebra of planar rooted trees and prove that these operads are Koszul.

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