Related papers: Combinatorics of exceptional sequences in type A
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
This is an expository paper which has two parts. In the first part, we study quiver varieties of affine $A$-type from a combinatorial point of view. We present a combinatorial method for obtaining a closed formula for the generating…
This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…
Let Q be a quiver of type ADE. We construct the corresponding Auslander-Reiten quiver as a topological complex inside the Coxeter complex associated with the underlying Dynkin diagram. We use the notion of chamber weights coming from the…
In our previous paper we studied non-semistable exceptional objects in hereditary categories and introduced the notion of regularity preserving category, but we obtained quite a few examples of such categories. Certain conditions on the…
We determine the probability distribution for relative projective objects in an exceptional sequence of type $A_n$ of any length. We show that these events (the $j$-th object in an exceptional sequence of length $k\le n$ being relatively…
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 potential, the exchange graph admits a natural acyclic…
We show that exceptional sequences for hereditary algebras are characterized by the fact that the product of the corresponding reflections is the inverse Coxeter element in the Weyl group. We use this result to give a new combinatorial…
This paper calculates the number of full exceptional collections modulo an action of a free abelian group of rank one for an abelian category of coherent sheaves on an orbifold projective line with a positive orbifold Euler characteristic,…
We study special linear systems called "very special" whose dimension does not satisfy a Clifford type inequality given by Huisman. We classify all these very special linear systems when they are compounded of an involution. Examples of…
Let $\Lambda$ be a finite-dimensional algebra over a field $K$. We describe how Buan and Marsh's $\tau$-exceptional sequences can be used to give a "brick labeling" of a certain poset of wide subcategories of finitely-generated…
We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded by an included linear series, whose number of base points…
Maximal green sequences were introduced as combinatorical counterpart for Donaldson-Thomas invariants for 2-acyclic quivers with potential by B. Keller. We take the categorical notion and introduce maximal green sequences for hearts of…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
This is a survey on the categorification of the poset of generalized non-crossing partitions, using the representation theory of a hereditary artin algebra H, looking at the set P of exceptional subcategories in mod H. This categorification…
As it is known, finitely presented quivers correspond to Dynkin graphs (Gabriel, 1972) and tame quivers -- to extended Dynkin graphs (Donovan and Freislich, Nazarova, 1973). In the article "Locally scalar reresentations of graphs in the…
The aim of this article is to study the Auslander algebra of any representation-finite string algebra. More precisely, we introduce the notion of gluing algebras and show that the Auslander algebra of a representation-finite string algebra…
Motivated by a construction in the theory of cluster algebras (Fomin and Zelevinsky), one associates to each acyclic directed graph a family of sequences of natural integers, one for each vertex; this construction is called a {\em frieze};…
For a stability condition $\sigma$ on a triangulated category, Dimitrov-Katzarkov introduced the notion of a $\sigma$-exceptional collection. In this paper, we study full $\sigma$-exceptional collections in the derived category of an…