Brick polytopes, lattice quotients, and Hopf algebras

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:155

Article

Pilaud, Vincent^1,2 

[1] Ecole Polytech, CNRS, Palaiseau, France

[2] Ecole Polytech, LIX, Palaiseau, France

关键词: Brick polytopes;    Multitriangulations;    Pipe dreams;    Combinatorial Hopf algebras;    Lattice quotients;   

DOI  :  10.1016/j.jcta.2017.11.014

来源: Elsevier

【 摘 要 】

This paper is motivated by the interplay between the Tamari lattice, J.-L. Loday's realization of the associahedron, and J.-L. Loday and M. Ronco's Hopf algebra on binary trees. We show that these constructions extend in the world of acyclic k-triangulations, which were already considered as the vertices of V. Pilaud and F. Santos' brick polytopes. We describe combinatorially a natural surjection from the permutations to the acyclic k-triangulations. We show that the fibers of this surjection are the classes of the congruence equivalent to(k) on S-n defined as the transitive closure of the rewriting rule UacV(1)b(1)V(k)b(k)W equivalent to(k) UcaV(1)b(1)V(k)b(k)W for letters a

【 授权许可】

Free