Enumerative combinatorics
A simple way to tell a simple polytope from its graph
Journal of Combinatorial Theory Series A
Hyperplane arrangements with a lattice of regions
Discrete & Computational Geometry
Handbook of combinatorics (vol. 2)
Generating trees and forbidden subsequences
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
Order Structure on the Algebra of Permutations and of Planar Binary Trees
Journal of Algebraic Combinatorics: An International Journal
Discrete Mathematics - Kleitman and combinatorics: a celebration
The order dimension of the poset of regions in a hyperplane arrangement
Journal of Combinatorial Theory Series A
The On-Line Encyclopedia of Integer Sequences
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Generalized descent patterns in permutations and associated Hopf algebras
European Journal of Combinatorics
Noncrossing partitions and the shard intersection order
Journal of Algebraic Combinatorics: An International Journal
The Hopf algebra of diagonal rectangulations
Journal of Combinatorial Theory Series A
European Journal of Combinatorics
Polyhedral models for generalized associahedra via Coxeter elements
Journal of Algebraic Combinatorics: An International Journal
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We give a unified explanation of the geometric and algebraic properties of two well-known maps, one from permutations to triangulations, and another from permutations to subsets. Furthermore we give a broad generalization of the maps. Specifically for any lattice congruence of the weak order on a Coxeter group we construct a complete fan of convex cones with strong properties relative to the corresponding lattice quotient of the weak order. We show that if a family of lattice congruences On the symmetric groups satisfies certain compatibility conditions then the family defines a sub Hopf algebra of the Malvenuto-Reutenauer Hopf algebra of permutations. Such a sub Hopf algebra has a basis which is described by a type of pattern avoidance. Applying these results. we build the Malvenuto Reutenauer algebra as the limit of an infinite sequence of smaller algebras.Where the second algebra in the sequence is the Hopf algebra of non-commutative symmetric functions. We also associate both a fan and a Hopf algebra to a set of permutations which appears to be equinumerous with the Baxter permutations.