7 papers · 1 filter
Invariance of rowmotion for variants of the Tamari lattice
Ben Adenbaum, Emily Barnard, Cesar Ceballos +6
We show that the rowmotion operator from dynamical algebraic combinatorics behaves the same on all alt -Tamari lattices for a fixed lattice path . We use this invariance of r…
Enumerating Pattern Avoiding Parking Functions
Ben Adenbaum
In this paper, we complete the enumeration of the number of parking functions of length avoiding, in the sense defined by Qiu and Remmel, a permutation of length 3, answering s…
The poset of maximal tubings of the cycle graph is a lattice
Ben Adenbaum, Emily Barnard, Max Hlavacek +4
The poset of maximal tubings of a graph generalizes several well-known and remarkable partial orders. Notable examples include the weak Bruhat order and the Tamari lattice, posets…
Dimensions of toggleability spaces
Ben Adenbaum, Spencer Daugherty, Nicholas Mayers
We establish a conjecture of Defant, Hopkins, Poznanović, and Propp concerning the dimensions of toggleability spaces for products of chains, shifted staircases, type-A root posets…
Boolean intervals in the weak Bruhat order of a finite Coxeter group
Ben Adenbaum, Jennifer Elder, Pamela E. Harris +1
Given a Coxeter group with Coxeter system , where is finite. We provide a complete characterization of Boolean intervals in the weak order of uniformly for all C…
Coloring Groups
Ben Adenbaum, Alexander Wilson
We introduce coloring groups, which are permutation groups obtained from a proper edge coloring of a graph. These groups generalize the generalized toggle groups of Striker (which…