arXiv subjects
Publications and source records attributed to Valcho Milchev.
This article examines the tilings of a strip with equilateral triangles. The number of ways in which the lattices can be covered with a combination of tiles of the two types of triangles is related to Pell's numbers. Additionally, the question of the number of tiles required for all possible tilings - both the number of tiles in total and by type - is developed for the first time in this article.
This article is dedicated to domino tilings of certain types of graph grids. For each of these grids, the domino tilings are represented using linear-recurrent sequences. New dependencies are proved that are not included in Neil Sloane's Online Encyclopedia of Integer Sequences (OEIS).
This article is dedicated to domino tilings of square grids. In each of these grids domino tilings are represented using linear-recurrent sequences. For different grids are determined new dependencies.
We study the possible positions of the Miquel point in the plane of a given triangle, which Miquel triangles are similar to the given one. We found out that these positions are eleven. We also study the possible positions of the Miquel point in the plane of a given triangle, where among the families of Miquel triangles there are triangles, which are similar to the given triangle. We study which of them are isogonal conjugated.