Comparing Diagonals on the Associahedra

2022/07/18 by Saneblidze, Samson, Umble, Ronald
#52B11 #55P99 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Primary 55P48 #Secondary 52B05

paper · doi:10.48550/arxiv.2207.08543

Abstract

We prove that the formula for the diagonal approximation Δ_K on J. Stasheff's n-dimensional associahedron K_n+2 derived by the current authors in 2004 agrees with the "magical formula" for the diagonal approximation Δ_K^′ derived by Markl and Shnider in 2006, by Loday in 2011, and by Masuda, Thomas, Tonks, and Vallette in 2021.

Related

• The diagonal of the associahedra
• A Diagonal on the Associahedra
• Three non-equivalent realizations of the associahedron
• Realization of the Stasheff polytope
• Celebrating Loday’s associahedron