11 citations · 60 across the 21 of their papers we have counts for
21 papers
Combinatorics of -Word Lattices
Henri Mühle
We study the -word lattices recently introduced by V. Pilaud and D. Poliakova in their study of generalized Hochschild polytopes. We prove that these lattices are extremal a…
Bubble Lattices II: Combinatorics
Thomas McConville, Henri Mühle
We introduce two simplicial complexes, the noncrossing matching complex and the noncrossing bipartite complex. Both complexes are intimately related to the bubble lattice introduce…
Bubble Lattices I: Structure
Thomas McConville, Henri Mühle
C. Greene introduced the shuffle lattice as an idealized model for DNA mutation and discovered remarkable combinatorial and enumerative properties of this structure. We attempt an…
Extremality, Left-Modularity and Semidistributivity
Henri Mühle
In this article we investigate the relations between three classes of lattices each extending the class of distributive lattices in a different way. In particular, we consider join…
Parabolic Tamari Lattices in Linear Type B
Wenjie Fang, Henri Mühle, Jean-Christophe Novelli
We study parabolic aligned elements associated with the type- Coxeter group and the so-called linear Coxeter element. These elements were introduced algebraically in (Mühle and…
- and -Triangles for -Associahedra
Cesar Ceballos, Henri Mühle
For any northeast path , we define two bivariate polynomials associated with the -associahedron: the - and the -triangle. We prove combinatorially that we can obtain on…
A Consecutive Lehmer Code for Parabolic Quotients of the Symmetric Group
Wenjie Fang, Henri Mühle, Jean-Christophe Novelli
In this article we define an encoding for parabolic permutations that distinguishes between parabolic -avoiding permutations. We prove that the componentwise order on these co…
The Rank Enumeration of Certain Parabolic Non-Crossing Partitions
Christian Krattenthaler, Henri Mühle
We consider -divisible non-crossing partitions of with the property that for some no block contains more than one of the first integers. We giv…
-Indivisible Noncrossing Partitions
Henri Mühle, Philippe Nadeau, Nathan Williams
For a fixed integer , we consider the set of noncrossing partitions, where both the block sizes and the difference between adjacent elements in a block is . We show th…
The Steep-Bounce Zeta Map in Parabolic Cataland
Cesar Ceballos, Wenjie Fang, Henri Mühle
As a classical object, the Tamari lattice has many generalizations, including -Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in…
Noncrossing Arc Diagrams, Tamari Lattices, and Parabolic Quotients of the Symmetric Group
Henri Mühle
Ordering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semid…
Tamari Lattices for Parabolic Quotients of the Symmetric Group
Henri Mühle, Nathan Williams
We generalize the Tamari lattice by extending the notions of -avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients of the sy…
Connectivity Properties of Factorization Posets in Generated Groups
Henri Mühle, Vivien Ripoll
We consider three notions of connectivity and their interactions in partially ordered sets coming from reduced factorizations of an element in a generated group. While one form of…
The Core Label Order of a Congruence-Uniform Lattice
Henri Mühle
We investigate the alternate order on a congruence-uniform lattice as introduced by N. Reading, which we dub the core label order of . When …
Trimness of Closed Intervals in Cambrian Semilattices
Henri Mühle
In this article, we give a short algebraic proof that all closed intervals in a -Cambrian semilattice are trim for any Coxeter group and any Coxeter element…
The -Cover Posets and Their Applications
Myrto Kallipoliti, Henri Mühle
In this article we introduce the -cover poset of an arbitrary bounded poset , which is a certain subposet of the -fold direct product of with itsel…
A Heyting Algebra on Dyck Paths of Type and
Henri Mühle
In this article we investigate the lattices of Dyck paths of type and under dominance order, and explicitly describe their Heyting algebra structure. This means that each D…
Towards m-Cambrian Lattices
Myrto Kallipoliti, Henri Mühle
For positive integers and , we introduce a family of lattices associated to the Cambrian lattice of the dihedral group .…
The Strip-Decomposition of m-Dyck Paths
Henri Mühle
The -Tamari lattices , introduced by Bergeron and Pr{é}ville-Ratelle, are defined as a poset of -Dyck paths equipped with the generalized rotation orde…
On the Topology of the Cambrian Semilattices
Myrto Kallipoliti, Henri Mühle
For an arbitrary Coxeter group , David Speyer and Nathan Reading defined Cambrian semilattices as semilattice quotients of the weak order on induced by certain semilat…
EL-Shellability and Noncrossing Partitions Associated with Well-Generated Complex Reflection Groups
Henri Mühle
In this article we prove that the lattice of noncrossing partitions is EL-shellable when associated with the well-generated complex reflection group of type , for $d,n\ge…