Nikolai Beluhov

collaborators

4 papers

math.CO2026

Translation Orders on Grids

Nikolai Beluhov

Let $S$ be a grid in $Z^{d}$ . We wish to order $S$ so that the way two points compare depends only on the offset between them. Does each such order arise from a linear funct…

math.CO2026

Powers of 2 in High-Dimensional Lattice Walks

Nikolai Beluhov

Let $W_{d} (n)$ be the number of $2 n$ -step walks in $Z^{d}$ which begin and end at the origin. We study the exponent of $2$ in the prime factorisation of this number; i.e., $w_…

math.CO2026

Bootstrap Percolation and Partial Difference Equations

Nikolai Beluhov

We study a bootstrap percolation process on $Z^{d}$ where each newly occupied point completes a copy of one of the patterns in some fixed collection $A$ . We aim, g…

math.CO2025

Powers of 2 in Balanced Grid Colourings

Nikolai Beluhov

Let $B (m, n)$ be the number of ways to colour a $2 m \times 2 n$ grid in black and white so that, in each row and each column, half of the cells are white and half are black. Bhattac…