3 papers
math.NT2026
Diamond Determinants and Somos Sequences
Nikolai Beluhov
A Somos sequence of order is defined by a quadratic recurrence of width . Some of the remarkable properties of these sequences for small are tied to certain matrices…
math.CO2025
Minimum-Turn Tours of Even Polyominoes
Nikolai Beluhov
Let be a connected bounded region in the plane formed out of blocks joined by their sides. Peng and Rascoussier conjectured that all minimum-turn Hamiltonian cycle…
math.CO2025
Double Tiles
Nikolai Beluhov
Which polygons admit two (or more) distinct lattice tilings of the plane? We call such polygons double tiles. It is well-known that a lattice tiling is always combinatorially isomo…