Related papers: Red sizes of quivers
We present a detailed model of the absolute number counts, color and redshift distributions of gravitational arclets observed in clusters of galaxies. The framework adopted for galaxy evolution is chosen to fairly reproduce the observed…
We establish a connection between knot theory and cluster algebras via representation theory. To every knot diagram (or link diagram), we associate a cluster algebra by constructing a quiver with potential. The rank of the cluster algebra…
This paper aims at robustly determining the redshift of the cluster of galaxies JKCS041 and at putting constraints on the formation epoch of the color-magnitude sequence in two very high redshift clusters. New deep z'-J data show a clear…
In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.
We initiate a study of the dependence on the choice of ground ring on the question of whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the cluster algebra and upper cluster algebra…
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
The cluster algebra of any acyclic quiver can be realized as the coordinate ring of a subvariety of a Kac-Moody group -- the quiver is an orientation of its Dynkin diagram, defining a Coxeter element and thereby a double Bruhat cell. We use…
We introduce mixed Segre numbers of ideals which generalize the notion of mixed multiplicities of ideals of finite colength and show how many results on mixed multiplicities can be extended to results on mixed Segre numbers. In particular,…
We give an example of a cluster-tilted algebra A with quiver Q, such that the associated cluster algebra has a denominator vector which is not the dimension vector of any indecomposable A-module. This answers a question posed by T.…
We previously reported a significant clustering of red galaxies (R-K=3.5--6) around the radio-loud quasar B2 1335+28 at z=1.086. In this paper, we establish the existence of a rich cluster at the quasar redshift, and study the properties of…
We apply our previous work on cluster characters for Hom-infinite cluster categories to the theory of cluster algebras. We give a new proof of Conjectures 5.4, 6.13, 7.2, 7.10 and 7.12 of Fomin and Zelevinsky's Cluster algebras IV for…
Dimensions like Gelfand, Krull, Goldie have an intrinsic role in the study of theory of rings and modules. They provide useful technical tools for studying their structure. In this paper we define one of the dimensions called couniserial…
We study the outskirts ($R<3R_{200c}$) of 40 groups and clusters of galaxies of the local Universe ($0.02<z<0.045$) with 300~km~s$^{-1}<\sigma<950$~km~s$^{-1}$. Using the SDSS DR10 catalog data, we measured the stellar mass of galaxy…
In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal…
Measurements of galaxy cluster abundances, clustering properties, and mass to- light ratios in current and future surveys can provide important cosmological constraints. Digital wide-field imaging surveys, the recently-demonstrated fidelity…
We obtain a bound on the number of solutions of $x^q=x$ in a finite noncommutative algebra over a field with $q$ elements. Furthermore, we completely characterize those rings for which this maximum number is attained.
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…
We establish that there is an algebraic number $\xi\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $\xi,$ there are only countably many less than $\xi$. Central to the…
Over the past few decades, there has been extensive research on scattered subspaces, partly because of their link to MRD codes. These subspaces can be characterized using linearized polynomials over finite fields. Within this context,…
Generalising a recent work of Dequ\^ene et al. on the connection between perfectly clustering words and band bricks over a particular family of gentle algebras, we characterise band bricks over string algebras whose underlying quiver is…