Related papers: On Maximal Green Sequences For Type A Quivers

We prove a version of Gabriel's theorem for (possibly infinite dimensional) representations of infinite quivers. More precisely, we show that the representation theory of quiver $\Omega$ is of unique type (each dimension vector has at most…

In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide…

Machine learning is becoming an increasingly valuable tool in mathematics, enabling one to identify subtle patterns across collections of examples so vast that they would be impossible for a single researcher to feasibly review and analyze.…

In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…

Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…

Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid…

A proper subsemigroup of a semigroup is maximal if it is not contained in any other proper subsemigroup. A maximal subsemigroup of a finite semigroup has one of a small number of forms, as described in a paper of Graham, Graham, and Rhodes.…

We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\times n$ matrices to (block) upper triangular matrices up to…

We extend recent work of the third author and Kouloukas by constructing deformations of integrable cluster maps corresponding to the Dynkin types $A_{2N}$, lifting these to higher-dimensional maps possessing the Laurent property and…

An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…

BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is…

We extend Carter's notion of admissible diagrams and attach a "Dynkin-like" diagram to each reduced reflection factorization of an element in a finite Weyl group. We give a complete classification for the diagrams attached to reduced…

For a finite dimensional hereditary algebra, we consider: exceptional sequences in the category of finite dimensional modules, silting objects in the bounded derived category, and m-cluster tilting objects in the m-cluster category. There…

This paper addresses the combinatorial structure of $m$-colored mutation classes. We provide an explicit and purely combinatorial description of the $m$-colored quivers that arise within the $m$-colored mutation class of a quiver of type…

In this article we construct a maximal set of kernels for a multi-parameter linear scale-space that allow us to construct trees for classification and recognition of one-dimensional continuous signals similar the Gaussian linear scale-space…

We consider Dynkin algebras, these are the hereditary artin algebras of finite representation type. The indecomposable modules for a Dynkin algebra correspond bijectively to the positive roots of a Dynkin diagram. Given a Dynkin algebra…

Cluster algebras, introduced by Fomin and Zelevinsky through the process of quiver mutation, have become central objects in modern algebra and geometry, linking combinatorial constructions with diverse mathematical domains such as…

A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…

We introduce diagrams for $m$-cluster categories which we call "horizontal" and "vertical" mutation fans. These are analogous to the mutation fans (also known as "semi-invariant pictures" or "scattering diagrams") for the standard ($m=1$)…

We discuss quiver gauge models with matter fields based on Dynkin diagrams of Lie superalgebra structures. We focus on A(1,0) case and we find first that it can be related to intersecting complex cycles with genus $g$. Using toric geometry,…