Related papers: Low upper bounds of ideals

We bound the number of minimal hypergraph transversals that arise in tri-partite 3-uniform hypergraphs, a class commonly found in applications dealing with data. Let H be such a hypergraph on a set of vertices V. We give a lower bound of…

The repetition threshold is the smallest real number $\alpha$ such that there exists an infinite word over a $k$-letter alphabet that avoids repetition of exponent strictly greater than $\alpha$. This notion can be generalized to graph…

A novel lower bound is introduced for the full rank probability of random finite field matrices, where a number of elements with known location are identically zero, and remaining elements are chosen independently of each other, uniformly…

We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$-compatible map for the pairs of a complete graph and an arbitrary graph, and using it, we give a combinatorial lower bound for the…

The concept of geometric-arithmetic index was introduced in the chemical graph theory recently, but it has shown to be useful. The aim of this paper is to obtain new inequalities involving the geometric-arithmetic index $GA_1$ and…

Known Bernstein-type upper bounds on the tail probabilities for sums of independent zero-mean sub-exponential random variables are improved in several ways at once. The new upper bounds have a certain optimality property.

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

This paper investigates t-reductions of ideals in pullback constructions. Section 2 examines the correlation between the notions of reduction and t-reduction in pseudo-valuation domains. Section 3 solves an open problem on whether the…

We initiate a study of algorithms with a focus on the computational complexity of individual elements, and introduce the fragile complexity of comparison-based algorithms as the maximal number of comparisons any individual element takes…

Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in…

We explicitly bound T-singularities on normal projective surfaces $W$ with one singularity, and $K_W$ ample. This bound depends only on $K_W^2$, and it is optimal when $W$ is not rational. We classify and realize surfaces attaining the…

Under ABC, Silverman showed that there are infinitely many non-Wieferich primes with respect to any (non-trivial) base $a$. Recently Srinivas and Subramani proved an analogous result over number fields with trivial class group. In the first…

We study the upper tail of the number of arithmetic progressions of a given length in a random subset of {1,...,n}, establishing exponential bounds which are best possible up to constant factors in the exponent. The proof also extends to…

We prove a conjectured lower bound of Nagel and Reiner on Betti numbers of edge ideals of bipartite graphs.

This note is devoted to show a simple proof of a tight lower bound of the parameterized compact set packing problem, based on ETH.

We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b \in R$ with $ab \in…

We give a lower bound on the probability of error in quantum state discrimination. The bound is a weighted sum of the pairwise fidelities of the states to be distinguished.

We determine upper bounds for the maximum order of an element of a finite almost simple group with socle T in terms of the minimum index m(T) of a maximal subgroup of T: for T not an alternating group we prove that, with finitely many…