Related papers: Complexity lower bound for typical right triangula…
We establish upper bounds for the complexity of Seifert fibered manifolds with nonempty boundary. In particular, we obtain potentially sharp bounds on the complexity of torus knot complements.
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the…
In this paper we show that in some cases the E.Hopf rigidity phenomenon admits quantitative interpretation. More precisely we estimate from above the measure of the set $\mathcal{M}$ swept by minimal orbits. These estimates are sharp, i.e.…
The arithmetic triangular billiards are classically chaotic but have Poissonian energy level statistics, in ostensible violation of the BGS conjecture. We show that the length spectra of their periodic orbits divides into subspectra…
This paper gives the linear complexity of binary Ding-Helleseth generalized cyclotomic sequences of any order.
We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value…
Barrier billiards are simple examples of pseudo-integrable models which form an appealing but poorly investigated subclass of dynamical systems. The paper examines the semiclassical limit of the exact quantum transfer operator for barrier…
We study outer billiards with contraction outside regular polygons. For regular $n$-gons with $n = 3, 4, 5, 6, 8$, and $12$, we show that as the contraction rate approaches $1$, dynamics of the system converges, in a certain sense, to that…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
The pseudo-Euclidean Toda-like system of cosmological origin is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the ``singularity'' is reduced to a billiard on the…
A simple graph is $3$-rigid if its generic bar-joint frameworks in $R^3$ are infinitesimally rigid. Necessary and sufficient conditions are obtained for the minimal $3$-rigidity of a simple graph which is obtained from the $1$-skeleton of a…
We show a local rigidity result for the integrability of symplectic billiards. We prove that any domain which is close to an ellipse, and for which the symplectic billiard map is rationally integrable must be an ellipse as well. This is in…
There are many "minimax" complexity functions in mathematics: width of a tree or a link, Heegaard genus of a 3-manifold, the Cheeger constant of a Riemannian manifold. We define such a function w, "width", on countable (or finite) groups…
This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds arise from varying hypotheses on the surface…
We consider classical billiards on surfaces of constant curvature, where the charged billiard ball is exposed to a homogeneous, stationary magnetic field perpendicular to the surface. We establish sufficient conditions for hyperbolicity of…
The complexities of self-dual normal bases, which are candidates for the lowest complexity basis of some defined extensions, are determined with the help of the number of all but the simple points in well chosen minimal Besicovitch…
We find some general lower bounds of the sum of certain families of multigraded Betti numbers of any simplicial complex with a vertex coloring.
We obtain a new lower bound on the radius of the largest ball of separable unnormalized states around the identity matrix for a 3-qubit system. This also enables us to improve the corresponding lower bounds for multi-qubit systems. These…
Triangular decomposition is one of the standard ways to represent the radical of a polynomial ideal. A general algorithm for computing such a decomposition was proposed by A. Szanto. In this paper, we give the first complete bounds for the…
We observe that a particular first integral of the partially-averaged system in the secular theory of the three-body problem appears also as an important conserved quantity of integrable Kepler billiards. In this note we illustrate their…