2011/01/07 by Adaricheva, Kira
#05A05 #06B99 #52B05 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1101.1536
An assosiahedron Kn, known also as Stasheff polytope, is a multifaceted combinatorial object, which, in particular, can be realized as a convex hull of certain points in Rn, forming (n-1)-dimensional polytope. A permutahedron Pn is a polytope of dimension (n-1) in Rn with vertices forming various permutations of n-element set. There exist well-known orderings of vertices of Pn and Kn that make these objects into lattices: the first known as permutation lattices, and the latter as Tamari lattices. We establish that the vertices of Kn can be naturally associated with particular vertices of Pn in such a way that the corresponding lattice operations are preserved. In lattices terms, Tamari lattices are sublattices of permutation lattices. More generally, this defines the application of associative law as a special form of permutation.