D. Krachun

activity

20182020

collaborators

4 papers

math.NT2020

On sums of four pentagonal numbers with coefficients

Dmitry Krachun, Zhi-Wei Sun

The pentagonal numbers are the integers given by $p_{5} (n) = n (3 n - 1) /2 (n = 0, 1, 2, \dots)$ . Let $(b, c, d)$ be one of the triples $(1, 1, 2), (1, 2, 3), (1, 2, 6)$ and $(2, 3, 4)$ . We show that eac…

math.MG2019

Triangles on $Z^{2}$ and sliding phenomenon

Dmitry Krachun

We confirm the list from \cite{MSS} of values $D$ for which the high-density hard-core model on $Z^{2}$ with exceptional distance $D$ has infinitely many extremal Gibbs stat…

math.NT2018

On some determinants involving Jacobi symbols

Dmitry Krachun, Fedor Petrov, Zhi-Wei Sun +1

In this paper we study some conjectures on determinants with Jacobi symbol entries posed by Z.-W. Sun. For any positive integer $n \equiv 3 (mod 4)$ , we show that $$(6,1)_n=[6,1]_n=(3,…

cs.DS2018

An Optimal Space Lower Bound for Approximating MAX-CUT

Michael Kapralov, Dmitry Krachun

We consider the problem of estimating the value of MAX-CUT in a graph in the streaming model of computation. At one extreme, there is a trivial $2$ -approximation for this problem t…

On sums of four pentagonal numbers with coefficients

Triangles on Z2 and sliding phenomenon

On some determinants involving Jacobi symbols

An Optimal Space Lower Bound for Approximating MAX-CUT

Triangles on $Z^{2}$ and sliding phenomenon