18 citations · 46 across the 8 of their papers we have counts for
17 papers
Maximal green sequences for string algebras
Alexander Garver, Khrystyna Serhiyenko
Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. The two fundamental questions about maximal green sequences are whether…
Combinatorics of Type D Exceptional Sequences
Emily Carrick, Alexander Garver
Exceptional sequences are important sequences of quiver representations in the study of representation theory of algebras. They are also closely related to the theory of cluster al…
Counting linear extensions of posets with determinants of hook lengths
Alexander Garver, Stefan Grosser, Jacob P. Matherne +1
We introduce a class of posets, which includes both ribbon posets (skew shapes) and -complete posets, such that their number of linear extensions is given by a determinant of a…
Minuscule reverse plane partitions via quiver representations
Alexander Garver, Rebecca Patrias, Hugh Thomas
The Hillman--Grassl correspondence is a well-known bijection between multisets of rim hooks of a partition shape and reverse plane partitions of . We use the tools of quiver…
Leading terms of web invariants
Véronique Bazier-Matte, Guillaume Douville, Alexander Garver +3
We use Khovanov and Kuperberg's web growth rules to identify the minimal term in the invariant associated to an web diagram, with respect to a particular term order.
Minuscule reverse plane partitions via quiver representations
Alexander Garver, Rebecca Patrias, Hugh Thomas
A nilpotent endomorphism of a quiver representation induces a linear transformation on the vector space at each vertex. Generically among all nilpotent endomorphisms, there is a we…
A categorification of biclosed sets of strings
Alexander Garver, Thomas McConville, Kaveh Mousavand
We consider the closure space on the set of strings of a gentle algebra of finite representation type. Palu, Pilaud, and Plamondon proved that the collection of all biclosed sets o…
Semistable subcategories for tiling algebras
Monica Garcia, Alexander Garver
Semistable subcategories were introduced in the context of Mumford's GIT and interpreted by King in terms of representation theory of finite dimensional algebras. Ingalls and Thoma…
The canonical join complex for biclosed sets
Alexander Clifton, Peter Dillery, Alexander Garver
The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give…
Greene--Kleitman invariants for Sulzgruber insertion
Alexander Garver, Rebecca Patrias
R. Sulzgruber's rim hook insertion and the Hillman-Grassl correspondence are two distinct bijections between the reverse plane partitions of a fixed partition shape and multisets o…
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…
Oriented Flip Graphs and Noncrossing Tree Partitions
Alexander Garver, Thomas McConville
In this paper, we study the lattice properties of posets of torsion pairs in the module category of a family of representation-finite gentle algebras called tiling algebras, introd…
Lattice Properties of Oriented Exchange Graphs and Torsion Classes
Alexander Garver, Thomas McConville
The exchange graph of a 2-acyclic quiver is the graph of mutation-equivalent quivers whose edges correspond to mutations. When the quiver admits a nondegenerate Jacobi-finite poten…
Combinatorics of exceptional sequences in type A
Alexander Garver, Kiyoshi Igusa, Jacob P. Matherne +1
Exceptional sequences are certain ordered sequences of quiver representations. We introduce a class of objects called strand diagrams and use this model to classify exceptional seq…
A Combinatorial Model for Exceptional Sequences in Type A
Alexander Garver, Jacob P. Matherne
Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work)…
On Maximal Green Sequences For Type A Quivers
Alexander Garver, Gregg Musiker
Given a framed quiver, i.e. one with a frozen vertex associated to each mutable vertex, there is a concept of green mutation, as introduced by Keller. Maximal sequences of such mut…