Report On Cobweb Posets' Tiling Problem

Responding to Kwaśniewski’s cobweb posets’ problems posed in [3, 4] we present here some results on one of them namely on Cobweb Tiling Problem. Kwaśniewski cobweb posets with tiling property are designated-coded by their correspondent tiling sequences. We show that the family of all cobweb tiling sequences includes Natural numbers, Fibonacci numbers, Gaussian integers and show that there are more other cobweb tiling sequences. We show also that cobweb tiling problem is a particular case of clique problem in a certain graph. To this end we illustrate the area of our reconnaissance by means of the Venn type map of various cobweb sequences families according to definitions from [3, 4].