Related papers: On mutation of {\tau}-tilting modules
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and…
In this paper we discuss dilaton shifts (Euler counterterms) arising in decomposition of two-dimensional quantum field theories with higher-form symmetries. These take a universal form, reflecting underlying (noninvertible, quantum)…
A general concept for the derivation of symmetry-based pseudo spin Hamiltonians is described. It systematically bridges the gap between the atomistic basis and various pseudo spin models presented in literature. It thus allows the…
Pull-tabbing is an evaluation approach for functional logic computations, based on a graph transformation recently proposed, which avoids making irrevocable non-deterministic choices that would jeopardize the completeness of computations.…
A permutation $\sigma$ of a multiset is called Stirling permutation if $\sigma(s)\ge \sigma(i)$ as soon as $\sigma(i)=\sigma(j)$ and $i<s<j.$ In our paper we study Stirling polynomials that arise in the generating function for descent…
This paper introduces two forms of modular inverses and proves their reciprocity formulas respectively. These formulas are then applied to formulate new and generalized algorithm for computing these modular inverses. The same algorithm is…
We study the module categories of a tilted algebra C and the corresponding cluster-tilted algebra B. In particular, we study which $\tau$-rigid C-modules are also $\tau$-rigid B-modules.
A transformation of morphisms of sheaves, called mutation, is used to build new moduli spaces of morphisms.
We discuss various formalisms to describe string-to-string transformations. Many are based on automata and can be seen as operational descriptions, allowing direct implementations when the input scanner is deterministic. Alternatively, one…
Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…
Comparing the module categories of an algebra and of the endomorphism algebra of a given support $\tau$-tilting module, we give a generalization of the Brenner-Butler's tilting theorem in the framework of $\tau$-tilting theory. Afterwards…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
Transmutation is a technique for extending classical probability distributions in order to give them more flexibility. In this paper, we are interested in cubic transmutations of the Pareto distribution. We establish a general formula that…
Let $\Gamma$ be a split extension of a finite-dimensional algebra $\Lambda$ by a nilpotent bimodule $_\Lambda E_\Lambda$, and let $(T,P)$ be a pair in $\mod\Lambda$ with $P$ projective. We prove that $(T\otimes_\Lambda \Gamma_\Gamma,…
Using the Weil-Brezin-Zak transform of solid state physics, we describe line bundles over elliptic curves in terms of Weyl operators. We then discuss the connection with finitely-generated projective modules over the algebra $A_\theta$ of…
Moving a module in a modular robot is a very complex and error-prone process. Unlike in swarm, in the modular robots we are targeting, the moving module must keep the connection to, at least, one other module. In order to miniaturize each…
We introduce the notions of t-lifting modules and t-dual Baer modules, which are generalizations of lifting modules. It is shown that an amply supplemented module $M$ is t-lifting if and only if $M$ is t-dual Baer and a…
A self-contained introduction to the basics of Tau-tilting theory. We assume that the reader is familiar with Auslander-Reiten theory, but circumvent the need for the Brenner-Butler tilting theorem completely.
Mutation testing is an effective technique for assessing the effectiveness of test suites by systematically injecting artificial faults into programs. However, existing mutation testing techniques fall short in capturing many types of…