Construct explicit higher coherences for associahedral and permutahedral diagonals

Construct explicit higher coherences correcting the non-coassociativity of the cellular diagonals for associahedra and permutahedra.

Background

Cellular diagonals for associahedra and permutahedra are not coassociative, unlike the corresponding diagonals for simplices and cubes. Higher coherences are therefore required to correct this failure of coassociativity. The paper studies the asymptotic length of associahedra and permutahedra as a measure of their non-shortness, but explicitly states that it does not advance the construction of these coherences.