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We show upper and lower bounds for angles in iterations of trisections of certain triangulations.

We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in…

Suppose $X$ is a uniformly distributed $n$-dimensional binary vector and $Y$ is obtained by passing $X$ through a binary symmetric channel with crossover probability $\alpha$. A recent conjecture by Courtade and Kumar postulates that…

This paper is devoted to the study of lower and upper bounds for the number of vertices of the polytope of $n\times n\times n$ stochastic tensors (i.e., triply stochastic arrays of dimension $n$). By using known results on polytopes (i.e.,…

Comments on extensions of Verma modules in the Bernstein-Gelfand-Gelfand Category O.

We obtain a non--trivial upper bound for the multiplicative energy of any sufficiently large subset of a subvariety of a finite algebraic group. We also find some applications of our results to growth of conjugates classes, estimates of…

We introduce a formalism which allows us to formulate a version of Fukaya category in presence of curves of higher genus.

We prove an improved form of an expectation of Polya and discuss several related questions

Assume G is a nilpotent group of class > 3 in which every proper subgroup has class at most 3. In this note, we give the exact upper bound of class of G.

This paper studies explicit and theoretical bounds for several interesting quantities in number theory, conditionally on the Generalized Riemann Hypothesis. Specifically, we improve the existing explicit bounds for the least quadratic…

In this article we present the idea of clique ceiling numbers of the vertices of a given graph that has a universal vertex. We follow up with a polynomial-time algorithm to compute an upper bound for the clique number of such a graph using…

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic…

We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.

We establish a quantitative lower bound on the reach of flat norm minimizers for boundaries in $\mathbb{R}^2$.

We obtain several new upper bounds of the odd graceful chromatic number of a graph $G$, which must be bipartite. Some of our bounds depend only on the number of the vertices of $G$ or the chromatic number of some graphs related to the…

We prove several extensions of the Erdos-Fuchs theorem.

A family of exact upper bounds interpolating between Chebyshev's and Cantelli's is presented.

We make explicit a theorem of Fromm and Goldmakher [arXiv:1706.03002], which states that one can improve Burgess' bound for short character sums simply by improving the leading constant in the P\'{o}lya-Vinogradov inequality. Towards…

It is established that for any finite set of positive real numbers $A$, we have $$|A/A+A| \gg \frac{|A|^{\frac{3}{2}+\frac{1}{26}}}{\log^{1/2}|A|}.$$

Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.