18 citations · 99 across the 31 of their papers we have counts for
32 papers
The Minkowski function and Salem's problem. II
Giedrius Alkauskas
In 1943, R. Salem asked whether the Fourier-Stieltjes transform of the Minkowski question-mark function vanishes at infinity. This problem was answered affirmatively by Jordan and…
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 --…
Squares, three fleas, sporadic sets, and squares
Giedrius Alkauskas
Three fleas are on the plane. At each move, two fleas jump to the other two vertices of a square erected on the segment joining them. Starting from , we ask…
Full Grid Lattice Polygons with Maximal Sum of Squares of Edge-Lengths
Oliver Mantas Ališauskas, Giedrius Alkauskas, Valdas Dičiūnas
Consider a subset [1,2,...,n]x[1,2,...,n] of the plane integer lattice. Take any non self-intersecting n^2-gon built on it (straight angles are allowed). The square of a side lengt…
Friendly paths for finite subsets of plane integer lattice. I
Giedrius Alkauskas
For a given finite subset P of points of the lattice Z^2, a friendly path is a monotone (uphill or downhill) lattice path which splits points in half; points lying on the path itse…
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