18 citations · 72 across the 12 of their papers we have counts for
19 papers · 1 filter
Extended Weak Order for the Rank 3 Universal Coxeter Group
Grant Barkley, Colin Defant, Patricia Hersh +3
The weak order is a classical poset structure on a Coxeter group; it is a lattice when the group is finite but merely a meet-semilattice when the group is infinite. Motivated by pr…
Hyperbinary partitions and q-deformed rationals
Thomas McConville, James Propp, Bruce E. Sagan
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of 2 and every part appears at most twice. We give three applications of the length…
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…
Determinantal formulas with major indices
Thomas McConville, Donald Robertson, Clifford Smyth
We give a simple proof of a major index determinant formula in the symmetric group discovered by Krattenthaler and first proved by Thibon using noncommutative symmetric functions.…
On a rank-unimodality conjecture of Morier-Genoud and Ovsienko
Thomas McConville, Bruce E. Sagan, Clifford Smyth
Let alpha = (a,b,...) be a composition. Consider the associated poset F(alpha), called a fence, whose covering relations are x_1 < x_2 < ... < x_{a+1} > x_{a+2} > ... > x_{a+b+1} <…
The facial weak order on hyperplane arrangements
Aram Dermenjian, Christophe Hohlweg, Thomas McConville +1
We extend the facial weak order from finite Coxeter groups to central hyperplane arrangements. The facial weak order extends the poset of regions of a hyperplane arrangement to all…
Roots of descent polynomials and an algebraic inequality on hook lengths
Pakawut Jiradilok, Thomas McConville
We prove a conjecture by Diaz-Lopez et al. that bounds the roots of descent polynomials. To do so, we prove an algebraic inequality, which we refer to as the "Slice and Push Inequa…
Lattices from graph associahedra and subalgebras of the Malvenuto-Reutenauer algebra
Emily Barnard, Thomas McConville
The Malvenuto-Reutenauer algebra is a well-studied combinatorial Hopf algebra with a basis indexed by permutations. This algebra contains a wide variety of interesting sub Hopf alg…
Zonotopes whose cellular strings are all coherent
Rob Edman, Pakawut Jiradilok, Gaku Liu +1
A cellular string of a polytope is a sequence of faces stacked on top of each other in a given direction. The poset of cellular strings, ordered by refinement, is known to be homot…
Root system chip-firing I: Interval-firing
Pavel Galashin, Sam Hopkins, Thomas McConville +1
Jim Propp recently introduced a variant of chip-firing on a line where the chips are given distinct integer labels. Hopkins, McConville, and Propp showed that this process is confl…
Root system chip-firing II: Central-firing
Pavel Galashin, Sam Hopkins, Thomas McConville +1
Jim Propp recently proposed a labeled version of chip-firing on a line and conjectured that this process is confluent from some initial configurations. This was proved by Hopkins-M…
Enumerative properties of Grid-Associahedra
Alexander Garver, Thomas McConville
We continue the study of the nonkissing complex that was introduced by Petersen, Pylyavskyy, and Speyer and was studied lattice-theoretically by the second author. We introduce a t…
Minimal length maximal green sequences
Alexander Garver, Thomas McConville, Khrystyna Serhiyenko
Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. It is an open problem to determine what lengths are achieved by the max…
Sorting via chip-firing
Sam Hopkins, Thomas McConville, James Propp
We investigate a variant of the chip-firing process on the infinite path graph: rather than treating the chips as indistinguishable, we label them with positive integers. To fire a…
Homotopy type of intervals of the second higher Bruhat orders
Thomas McConville
The higher Bruhat order is a poset of cubical tilings of a cyclic zonotope whose covering relations are cubical flips. For a 2-dimensional zonotope, the higher Bruhat order is isom…
Lattice structure of Grid-Tamari orders
Thomas McConville
The Tamari order is a central object in algebraic combinatorics and many other areas. Defined as the transitive closure of an associativity law, the Tamari order possesses a surpri…
Biclosed sets in real hyperplane arrangements
Thomas McConville
The set of chambers of a real hyperplane arrangement may be ordered by separation from some fixed chamber. When this poset is a lattice, Bjorner, Edelman, and Ziegler proved that t…
Crosscut-simplicial Lattices
Thomas McConville
We call a lattice crosscut-simplicial if the crosscut complex of every atomic interval is equal to the boundary of a simplex. Every interval of such a lattice is either contractibl…