Related papers: The Moore Bound for Regular Simplicial Complexes
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
We give a topological bound on the number of minimal models of a class of three dimensional log smooth pairs of general type.
A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…
We show there is an upper bound on the diameter of a closed, hyperbolic 3-manifold in terms of the length of any presentation of its fundamental group.
Let $R$ be a commutative ring. We show that pure injective resolutions and pure projective resolutions can be constructed for unbounded complexes of $R$-modules. We use these to obtain a closed symmetric monoidal structure on the unbounded…
Algebraic surfaces in the complex projective space with a high number of A-type singularities have been presented in a recent paper. We extend the construction in order to obtain lower bounds for the maximal number of A singularities for…
We obtain lower bounds for the maximum dimension of a simple FG-module, where G is a finite group and F is an algebraically closed field of characteristic p. The bounds are described in terms of properties of p-subgroups of G. When p is 2…
We provide a lower bound on the complexity function of a typical (in the Lebesgue measure sence) right triangular billiard.
This paper is concerned with the combinatorial description of the graded minimal free resolution of certain monomial algebras which includes toric rings. Concretely, we explicitly describe how the graded minimal free resolution of those…
We give a general method for proving quantum lower bounds for problems with small range. Namely, we show that, for any symmetric problem defined on functions $f:\{1, ..., N\}\to\{1, ..., M\}$, its polynomial degree is the same for all…
We obtain a series of results in the global theory of free boundary minimal surfaces, which in particular provide a rather complete picture for the way different complexity criteria, such as area, topology and Morse index compare, beyond…
We establish asymptotic upper bounds on the number of zeros modulo $p$ of certain polynomials with integer coefficients, with $p$ prime numbers arbitrarily large. The polynomials we consider have degree of size $p$ and are obtained by…
We show that the Rouquier dimension of the category of perfect complexes over a regular ring is precisely the Krull dimension of the ring. Previously, it was known that the Krull dimension is an upper bound, the lower bound however was not…
We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.
In this article we obtain an improved upper bound for the regularity of binomial edge ideals of trees.
We show a general lower bound for Mean-value of Dirichlet polynomials
In this note, we extend diameter bounds of Simon, Topping, and Wu--Zheng to submanifolds with boundary and (potentially non-compact) ambient manifolds with minor curvature restrictions. The bound is dependent on both an integral of mean…
The theoretical and practical aspects of the fundamental, ultimate, physical limits to scaling, or Moore-s law, is presented.
Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…
We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower…