Related papers: Bounds on numerical boundary slopes for Montesinos…

The slope conjecture gives a precise relation between the degree of the colored Jones polynomial of a knot and the boundary slopes of essential surfaces in the knot complement. In this note we propose a generalization of the slope…

We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examples of Shimura curves that do not descend over their field…

Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…

We derive upper and lower bounds on the sum of distances of a spherical code of size $N$ in $n$ dimensions when $N\sim n^\alpha, 0<\alpha\le 2.$ The bounds are derived by specializing recent general, universal bounds on energy of spherical…

We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…

In this article we obtain an improved upper bound for the regularity of binomial edge ideals of trees.

We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.

We show that the cusp volume of a hyperbolic alternating knot can be bounded above and below in terms of the twist number of an alternating diagram of the knot. This leads to diagrammatic estimates on lengths of slopes, and has some…

We establish a lower bound on the forcing numbers of domino tilings computable in polynomial time based on height functions. This lower bound is sharp for a 2n by 2n square as well as other cases.

For any number field k, upper bounds are established for the number of k-rational points of bounded height on non-singular del Pezzo surfaces defined over k, which are equipped with suitable conic bundle structures over k.

We give the bridge indices for 11-crossing prime knots and give a minimal bridge projection for each of these knots. The results on the indices may be easily summarized: all of these knots that are not rational knots or Montesinos knots…

We establish some bounds on the number of higher-dimensional partitions by volume. In particular, we give bounds via vector partitions and MacMahon's numbers.

We study the double slice genus of a knot, a natural generalization of slice genus. We define a notion called band number, a natural generalization of band unknotting number, and prove it is an upper bound on double slice genus. Our bound…

The problem of percolation along sites of square lattice is studied. The number of contours being external boundaries for finite clusters has been estimated using geometric considerations. This estimation makes it possible to determine more…

Knot mosaics are used to model physical quantum states. The mosaic number of a knot is the smallest integer $m$ such that the knot can be represented as a knot $m$-mosaic. In this paper we establish an upper bound for the crossing number of…

We provide an upper bound for the genus zero logarithmic Gromov-Witten invariants of projective space relative to its toric boundary. The upper bound is polynomial in the contact orders, with degree depending on the number of marked points.…

We give an upper bound for the number of cusps of a plane affine or projective curve via its first Betti number.

We give upper bounds on the size of the gap between a non-zero constant term and the next non-zero Fourier coefficient of an entire level two modular form. We give upper bounds for the minimum positive integer represented by a level two…

In this paper, we obtain the sharp upper and lower bounds for the spectral radius of a nonnegative irreducible matrix. We also apply these bounds to various matrices associated with a graph or a digraph, obtain some new results or known…

We prove new bounds on the number of incidences between points and higher degree algebraic curves. The key ingredient is an improved initial bound, which is valid for all fields. Then we apply the polynomial method to obtain global bounds…