Fault free tilings

Abstract:Fault-free tilings are a class of tiling problems that deal with tilings with no fault lines, that is, no lines along the columns or rows can be drawn across the board without intersecting some tile. Though these type of tilings are interesting to study, not much progress has been made in this field. In this talk, we will discuss the very first paper on fault-free tilings by R.L.Graham. Moreover, we will point out some questions that arise while studying fault-free tilings but have gone unanswered till date, and we will also try to point out the progress that have been made in the field of fault-free tilings but will however, not discuss those papers at length.