The \(s\)-weak order and \(s\)-permutahedra. I: Combinatorics and lattice structure

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Structure theory of lattices (06B05) Lattice ideals, congruence relations (06B10)

Cites Work

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Associahedra, Tamari lattices and related structures. Tamari memorial Festschrift
The algebra of binary search trees
Permutahedra and generalized associahedra.
The number of intervals in the \(m\)-Tamari lattices
Splitting lattices generate all lattices
Hopf algebra of the planar binary trees
Conjectures on the quotient ring by diagonal invariants
On permutation lattices
Cluster algebras. II: Finite type classification
Order structure on the algebra of permutations and of planar binary trees
Cayley lattices of finite Coxeter groups are bounded
Poset topology of \(s\) weak order via SB-labelings
The \(\nu \)-Tamari lattice via \(\nu \)-trees, \( \nu \)-bracket vectors, and subword complexes
The \(s\)-weak order and \(s\)-permutahedra
Hopf algebras of \(m\)-permutations, \((m + 1)\)-ary trees, and \(m\)-parking functions
Signature Catalan combinatorics
Structure of the Loday-Ronco Hopf algebra of trees.
Realizations of the associahedron and cyclohedron
The representation of the symmetric group on \(m\)-Tamari intervals
Higher trivariate diagonal harmonics via generalized Tamari posets
Lattice and order properties of the poset of regions in a hyperplane arrangement
Cambrian lattices.
Lattice congruences of the weak order.
On the number of intervals in Tamari lattices
Hilbert schemes, polygraphs and the Macdonald positivity conjecture
Cluster algebras. I: Foundations
A lattice on decreasing trees: the metasylvester lattice
Lattice Theory of the Poset of Regions
Characterizations of Finite Lattices that are Bounded-Homomqrphic Images or Sublattices of Free Lattices
Shellable nonpure complexes and posets. II
THE LATTICE OF PERMUTATIONS IS BOUNDED
Quotientopes
A graded representation model for Macdonald's polynomials.
The enumeration of generalized Tamari intervals
The enumeration of generalized Tamari intervals
Permutrees
Celebrating Loday's associahedron
Hopf dreams and diagonal harmonics

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