Related papers: Bounds on numerical boundary slopes for Montesinos…
We show upper and lower bounds for angles in iterations of trisections of certain triangulations.
Let K be a tame knot with irreducible exterior M(K) in a closed, connected, orientable 3--manifold Sigma such that pi_1(Sigma) is cyclic. If infinity is not a strict boundary slope, then the diameter of the set of strict boundary slopes of…
We prove an asymptotic formula for the number of integral points of bounded log-anticanonical height on split smooth quintic del Pezzo surfaces over number fields, with respect to one of the lines as the boundary divisor.
We give upper and lower bounds on the leading coefficients of the $L^2$-Alexander torsions of a $3$-manifold $M$ in terms of hyperbolic volumes and of relative $L^2$-torsions of sutured manifolds obtained by cutting $M$ along certain…
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of the integers and certain subdeterminants of the constraint…
New lower bounds on the unknotting number of a knot are constructed from the classical knot signature function. These bounds can be twice as strong as previously known signature bounds. They can also be stronger than known bounds arising…
We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons},…
We show that a lower bound for covariance of $\min(X_1,X_2)$ and $\max(X_1,X_2)$ is $\cov{X_1}{X_2}$ and an upper bound for variance of \\ $\min(X_2,\max(X,X_1))$ is $\var{X} + \var{X_1} +\var{X_2}$ generalizing previous results. We also…
Given a fractional differential equation of order $\alpha \in (0,1]$ with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respective initial conditions. Specifically, we look at two…
We define and study Vassiliev invariants for (long) Morse knots. It is shown that there are Vassiliev invariants which can distinguish some topologically equivalent Morse knots. In particular, there is an invariant of order 3 for Morse…
We prove an upper bound of $n+9$ for the strong separation number of the complete graph $K_n$, and an upper bound of $n+1$ for its weak separation number. This improves on the previous best known bound of $(1+o(1))n$ for both cases.
We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and…
In this note we apply a spectral method to the graph of alternating bilinear forms. In this way, we obtain upper bounds on the size of an alternating rank-metric code for given values of the minimum rank distance. We computationally compare…
Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven…
We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we show that this bound is strong enough to obtain the…
We prove a Chernoff-type upper variance bound for the multinomial and the negative multinomial distribution. An application is also given.
In this paper, we obtain two spectral upper bounds for the $k$-independence number of a graph which is is the maximum size of a set of vertices at pairwise distance greater than $k$. We construct graphs that attain equality for our first…
We introduce twelve polynomial invariants for long virtual knots, called intersection polynomials, extending and refining the three intersection polynomials for virtual knots. They are defined via intersection numbers of cycles on a closed…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
We introduce three kinds of invariants of a virtual knot called the first, second, and third intersection polynomials. The definition is based on the intersection number of a pair of curves on a closed surface. The calculations of…