Hopf algebras on decorated noncrossing arc diagrams

Abstract

Noncrossing arc diagrams are combinatorial models for the equivalence classes of the lattice congruences of the weak order on permutations. In this paper, we provide a general method to endow these objects with Hopf algebra structures. Specific instances of this method produce relevant Hopf algebras that appeared earlier in the literature.

15 pages, 6 figures; Version 2: exposition improvements

References in corpus (3)

• Algebraic and combinatorial structures on pairs of twin binary trees
• Brick polytopes, lattice quotients, and Hopf algebras
• Combinatorial Realization of the Hopf Algebra of Sashes

Cited by in corpus (1)

• Shard polytopes