7 citations · 31 across the 15 of their papers we have counts for
16 papers · 1 filter
On two-toned tilings and -words
Henri Mühle
In this article, we describe an explicit bijection between the set of -words as defined by Pilaud and Poliakova and the set of of two-toned tilings of a strip of length $m+n…
Refined Lattice Path Enumeration and Combinatorial Reciprocity
Henri Mühle, Eleni Tzanaki
It is well known that the set of -Dyck paths with a fixed height and a fixed amount of valleys is counted by the Fuß-Narayana numbers. In this article, we consider the set of $m…
Revisiting Generalizations of the Dehn--Sommerville Relations
Cesar Ceballos, Henri Mühle
We revisit several known versions of the Dehn--Sommerville relations in the context of: homology manifolds, semi-Eulerian complexes, general simplicial complexes, balanced semi-Eul…
Hochschild lattices and shuffle lattices
Henri Mühle
In his study of a Hochschild complex arising in connection with the free loop fibration, S. Saneblidze defined the freehedron, a certain polytope constructed via a truncation proce…
Meet-Distributive Lattices have the Intersection Property
Henri Mühle
Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator with the so-called anti-exchange propert…
A Poset Structure on the Alternating Group Generated by 3-Cycles
Henri Mühle, Philippe Nadeau
We investigate the poset structure on the alternating group that arises when the latter is generated by 3-cycles. We study intervals in this poset and give several enumerative resu…
Two Posets of Noncrossing Partitions Coming From Undesired Parking Spaces
Henri Mühle
Consider the noncrossing set partitions of an -element set which either do not contain the block , or which do not contain the singleton block whenever an…
Symmetric Decompositions and the Strong Sperner Property for Noncrossing Partition Lattices
Henri Mühle
We prove that the noncrossing partition lattices associated with the complex reflection groups for admit symmetric decompositions into Boolean subposets. As…
On the Poset of Multichains
Henri Mühle
In this note we introduce the poset of -multichains of a given poset . Its elements are the multichains of consisting of elements, and its partial…
Finite Dismantlable Semidistributive Lattices are Planar
Henri Mühle
In this article, we prove that finite semidistributive lattices are dismantlable if and only if they are planar. This extends a well-known result by Kelly and Rival that states the…
SB-Labelings, Distributivity, and Bruhat Order on Sortable Elements
Henri Mühle
In this article, we investigate the set of -sortable elements, associated with a Coxeter group and a Coxeter element , under Bruhat order, and we denote this poset b…
On Reflection Orders Compatible with a Coxeter Element
Henri Mühle
In this article we give a simple, almost uniform proof that the lattice of noncrossing partitions associated with a well-generated complex reflection group is lexicographically she…
Structural Properties of the Cambrian Semilattices -- Consequences of Semidistributivity
Henri Mühle
The -Cambrian semilattices defined by Reading and Speyer are a family of meet-semilattices associated with a Coxeter group and a Coxeter element , an…
Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details
Henri Mühle
A proper merging of two disjoint quasi-ordered sets and is a quasi-order on the union of and such that the restriction to or yields the original quasi-order…
Counting Proper Mergings of Chains and Antichains
Henri Mühle
A proper merging of two disjoint quasi-ordered sets and is a quasi-order on the union of and such that the restriction to and yields the original quasi-orde…
The Topology of the -Tamari Lattices
Henri Mühle
The -Tamari lattices were recently introduced by Bergeron and Préville-Ratelle as posets on -Dyck paths, and it was shown by Bousquet-Mélou, Fusy and…