Luks’s algorithm (JCSS 1982) to test isomorphism of bounded degree graphs in polynomial time is one of the most important results in the context of the Graph Isomorphism Problem and has been repeatedly used as a basic building block for many other algorithms. In particular, for graphs of logarithmic degree, Babai’s quasipolynomial isomorphism test (STOC 2016) essentially boils down to Luks’s al...

the aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]. in [1], ungar and chen showed that the algebra of the group sl(2,c) naturally leads to the notion of gyrogroups and gyrovector spaces for dealing with the lorentz group and its underlying hyperbolic geometry. they defined the chen addition and then chen model of hyperbolic geometry. in this paper,...

A category is described to which the Cuntz semigroup belongs and as a functor into which it preserves inductive limits. 1. Recently, Toms in [26] used the refinement of the invariant K0 introduced by Cuntz almost thirty years ago in [4] to show that certain C*-algebras are not isomorphic. Anticipating the possible use of this invariant to establish isomorphism, we take the liberty of reporting ...

A tournament is a graph in which each pair of distinct vertices is connected by exactly one directed edge. Tournaments are an important graph class, for which isomorphism testing seems to be easier to compute than for the isomorphism problem of general graphs. We show that tournament isomorphism and tournament automorphism is hard under DLOGTIME uniform AC many-one reductions for the complexity...

Let C be a category. A functor F : C → Sets is called representable if there exists an object B = BF in C with the property that there is a natural isomorphism of functors φ : C(−, BF ) −→ F. Thus, for every object X in C, there is an isomorphism φX from the set of arrows C(X,BF ) to the value F (X) of the functor. The naturality condition states that for any map f : Y → X in C, the identity F ...

The fusion of two Mirkovic-Vilonen cycles is a degeneration their product, defined using the Beilinson-Drinfeld Grassmannian. In this paper, we put in place conceptually elementary approach to computing product type $A$. We do so by transferring problem generalized orbital varieties Mirkovic-Vybornov isomorphism. As an application, explicitly compute all cluster exchange relations coordinate ri...

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

We compute the monoid V (LK(E)) of isomorphism classes of finitely generated projective modules over certain graph algebras LK(E), and we show that this monoid satisfies the refinement property and separative cancellation. We also show that there is a natural isomorphism between the lattice of graded ideals of LK(E) and the lattice of order-ideals of V (LK(E)). When K is the field C of complex ...