M. Shkolnikov

activity

20102026

most citedSelf-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry

24 citations · 108 across the 21 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.CO2017★ 10 cited

Sandpile solitons via smoothing of superharmonic functions

Nikita Kalinin, Mikhail Shkolnikov

Let $F : Z^{2} \to Z$ be the pointwise minimum of several linear functions. The theory of smoothing of integer-valued superharmonic function allows us to prove that unde…

math.NT2017

Tropical formulae for summation over a part of SL(2, Z)

Nikita Kalinin, Mikhail Shkolnikov

Let $f (a, b, c, d) = a^{2} + b^{2} + c^{2} + d^{2} - (a + c)^{2} + (b + d)^{2}$ , let $(a, b, c, d)$ stand for $a, b, c, d \in Z_{\geq 0}$ such that $a d - b c = 1$ . Define \begin{equation} \label{…

math.CO2017★ 9 cited

Introduction to tropical series and wave dynamic on them

Nikita Kalinin, Mikhail Shkolnikov

The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dy…

math.NT2017★ 1 cited

The number $π$ and summation by $S L (2, Z)$

Nikita Kalinin, Mikhail Shkolnikov

We obtained a new formula for $π$ .

Sandpile solitons via smoothing of superharmonic functions

Tropical formulae for summation over a part of SL(2, Z)

Introduction to tropical series and wave dynamic on them

The number π and summation by SL(2,Z)

The number $π$ and summation by $S L (2, Z)$