Related papers: Orientals and cubes, inductively

We classify primitive, rank 1, omega-categorical structures having polynomially many types over finite sets. For a fixed number of 4-types, we show that there are only finitely many such structures and that all are built out of finitely…

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

The cone of a classical group $G$ is an affine $G\times G$-variety. The aim of this note is to initiate its combinatorial study in the cases when $G$ is the complex orthogonal or symplectic group. The coordinate ring of the cone of $G$ is a…

Let $S$ be a finitely generated abelian semigroup of invertible linear operators on a finite dimensional real or complex vector space $V$. We show that every coarsely dense orbit of $S$ is actually dense in $V$. More generally, if the orbit…

Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained as the quotient of E3 by such a group. The cubic…

We construct several examples of compactification of Type IIB theory on orientifolds and discuss their duals. In six dimensions we obtain models with $N=1$ supersymmetry, multiple tensor multiplets, and different gauge groups. In nine…

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…

If $K$ and $L$ are mutually dual closed convex cones in a Hilbert space with the metric projections onto them denoted by $P_K$ and $P_L$ respectively, then the following two assertions are equivalent: (i) $P_K$ is isotone with respect to…

Rationally convex topological embeddings of compact surfaces (closed or with boundary) into $\mathbb{C}^2$ are constructed.

We discuss the structure of the derived category of coherent sheaves on cubic fourfolds of three types: Pfaffian cubics, cubics containing a plane and singular cubics, and discuss its relation to the rationality of these cubics.

The successful development and optimisation of optically-driven micromachines will be greatly enhanced by the ability to computationally model the optical forces and torques applied to such devices. In principle, this can be done by…

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…

Generalizing the octahedral configuration of six congruent cylinders touching the unit sphere, we exhibit configurations of congruent cylinders associated to a pair of dual Platonic bodies.

The article studies power complexes and generalized power complexes, and investigates the algebraic structure of their automorphism groups. The combinatorial incidence structures involved are cube-like, in the sense that they have many…

We describe the second order ODE's cubic in the first order derivative with 2-dimensional symmetry algebra. We show that there exist only eight different types of them. We also construct the easily verifiable Equivalence Criterion for every…

We consider "cubes" in products of finite cyclic groups and we study their tiling and spectral properties. (A set in a finite group is called a tile if some of its translates form a partition of the group and is called spectral if it admits…

We consider triangulations of closed $2$-dimensional (not necessarily orientable) surfaces. Any minimal set of zigzags that double covers the set of edges provides a $z$-orientation of the triangulation. We introduce Markov chains of…

Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…

In the present paper, we introduce and study oriented Getzler-Kapranov complexes. These complexes are generalizations of S. Merkulov's oriented graph complex. We investigate their relation to the cohomology of moduli spaces of complex and…

We propose a convenient category for directed homotopy consisting of preordered topological spaces generated by cubes. Its main advantage is that, like the category of topological spaces generated by simplices suggested by J. H. Smith, it…