Related papers: Comment on "Two notes on imbedded prime divisors"

The purpose of this note is to give a new, short proof of a classification of ACM sets of points in $P^1XP^1$ in terms of separators.

There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.

This note presents an interesting counterexample to a basic covering problem.

An observation on Hall-Littlewood polynomials.

We show that if $G$ is any $p$-group of class at most two and exponent $p$, then there exist groups $G_1$ and $G_2$ of class two and exponent $p$ that contain $G$, neither of which can be expressed as a central product, and with $G_1$…

The purpose of this short note is to show how it is possible to combine existing results in the literature to get the unique continuation from sets of positive measure for time dependent parabolic equations with Lipschitz principal part and…

These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

We improve known upper bounds for the minimal dispersion of a point set in the unit cube and its inverse in both the periodic and non-periodic settings. Some of our bounds are sharp up to logarithmic factors.

This paper has been withdrawn by the authors due to crucial error on assumption in Eq. 2. We cannot assume v_R and v_L to be equal or even have the same sign.

This note is an addendum to [1,2], pointing out the differences between these papers and raising open questions.

The aim of this note is two-fold. In the first part of the paper we are going to investigate an inverse problem related to additive energy. In the second, we investigate how dense a subset of a finite structure can be for a given additive…

Asymptotic properties of certain arithmetic functions involving exponential divisors are investigated.

We continue the work of [4, 2, 3], in which we discuss published assertions that are incorrect or incorrectly proven; that are severely limited or reduce to triviality; or that we improve upon.

We show that cores of ideals do not preserve the inclusion.

We appended an errata to the original submission. The purpose of this errata is to point out two errors in [2] and give a weakened version of those statements made.

We prove that, if $x$ and $q\leqslant x^{1/16}$ are two parameters, then for any invertible residue class $a$ modulo $q$ there exists a product of exactly three primes, each one below $x^{1/3}$, that is congruent to $a$ modulo $q$.

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

A conjecture regarding the structure of expander graphs is discussed.

This Reply to preceding Comment of arXiv:1909.09867 shows why the statements in the Comment are misleading. We point out that our physical picture and theirs are fundamentally different, therefore the claim of using their correlation to…