Two lower bounds for self-assemblies at temperature 1

Abstract—Using the Tile Assembly Model proposed by Rothemund and Winfree, we give two lower bounds on the minimum number of tile types needed to uniquely assemble a shape at temperature 1 under a natural assumption that there are no binding domain mismatches (any two adjacent tiles either form a bond or else both touching sides of the tiles are without glues). Rothemund and Winfree showed that uniquely assembling a full N × N square (a square where there is a bond between any two adjacent tiles) at temperature 1 requires N2 distinct tile types, and conjectured that the minimum number of tile types needed to

• Type: Conference
• Year: 2009
• Where: SAC
• Authors: Ján Manuch, Ladislav Stacho, Christine Stoll
• Keywords: Adjacent Tiles, Applied Computing, SAC 2009, Tile Assembly Model, Tile Types