The Hopf algebra of generic rectangulations
Combinatorics
2019-03-26 v1
Abstract
A family of permutations called 2-clumped permutations forms a basis for a sub-Hopf algebra of the Malvenuto-Reutenauer Hopf algebra of permutations. The 2-clumped permutations are in bijection with certain decompositions of a square into rectangles, called generic rectangulations. Thus, we can describe the Hopf algebra of 2-clumped permutations using generic rectangulations (we call this isomorphic Hopf algebra the Hopf algebra of generic rectangulations). In this paper, we describe the cover relations in a lattice of generic rectangulations that is a lattice quotient of the right weak order on permutations. We then use this lattice to describe the product and coproduct operations in the Hopf algebra of generic rectangulations.
Keywords
Cite
@article{arxiv.1903.09874,
title = {The Hopf algebra of generic rectangulations},
author = {Emily Meehan},
journal= {arXiv preprint arXiv:1903.09874},
year = {2019}
}