18 citations · 46 across the 8 of their papers we have counts for
9 papers · 1 filter
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…
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…
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)…