相关论文: Maximal green sequences for string algebras
This paper investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalizes…
We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the…
Superspecies are introduced to provide the nice constructions of all finite-dimensional superalgebras. All acyclic superspecies, or equivalently all finite-dimensional (gr-basic) gr-hereditary superalgebras, are classified according to…
In this paper, we give a description of the self-injective dimension of string algebras and obtain a necessary and sufficient condition for a string algebra to be Gorenstein.
A matching $M$ of a graph $G$ is maximal if it is not a proper subset of any other matching in $G$. Maximal matchings are much less known and researched than their maximum and perfect counterparts. In particular, almost nothing is known…
We explicitly present expansions of the complex field which are models of the theories of green points in the multiplicative group case and in the case of an elliptic curve without complex multiplication defined over $\mathbb{R}$. In fact,…
This paper investigates the relationships between closed and mixed string amplitudes at the tree level in string theory. Through the analytic continuation of complex variables, we establish a factorization of closed string amplitudes into…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
One cannot yet point to any firm string prediction. While many approximate string ground states are known with interesting properties, we do not have any argument that one or another describes what we observe around us, and for reasons…
Maximal green sequences are particular sequences of mutations of quivers which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-C\'ordova-Vafa in the context of supersymmetric gauge…
On-shell superspace techniques are used to quantify R-symmetry violation in type IIB superstring theory amplitudes in a flat background in ten dimensions. This shows the existence of a particularly simple class of non-vanishing amplitudes…
New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> makes an important such contribution.
There are various reasons why adding stubs to the vertices of open string field theory (OSFT) is interesting: Not only the stubs can tame certain singularities and make the theory more well-behaved, but also the new theory shares a lot of…
We consider the problem of sequencing a set of positive numbers. We try to find the optimal sequence to maximize the variance of its partial sums. The optimal sequence is shown to have a beautiful structure. It is interesting to note that…
The application of the max-algebra to describe queueing systems by both linear scalar and vector equations is discussed. It is shown that these equations may be handled using ordinary algebraic manipulations. Examples of solving the…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…
How we choose to represent our data has a fundamental impact on our ability to subsequently extract information from them. Machine learning promises to automatically determine efficient representations from large unstructured datasets, such…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…
These four lectures, addressed to an audience of graduate students in experimental high energy physics, survey some of the basic concepts in string theory. The purpose is to convey a general sense of what string theory is and what it has…