3 papers
math.CO2026
Regular triangle unions with maximal number of sides
Giedrius Alkauskas
Fix an integer n>=1. Suppose that a simple polygon is the union of n triangles whose vertices along the common boundary are arranged cyclically. How many sides can such a union --…
math.NT2025
Squares, three fleas, sporadic integer sets, and squares
Giedrius Alkauskas
In the plane, three integer points ("fleas") are given. At every tick of time, two of them (say, P,Q) instantly jump to two vacant points R,S, so that PQRS is a square with that or…
math.CO2025
Colouring monohedral tilings: defects and grain boundaries
Giedrius Alkauskas
In this paper it is proved that there exist periodic monohedral tilings and finite seeds of colored tiles, which force non-periodic coloring of the whole plane