Area of math dealing with sliding tiles?

Question

I am not sure if this may be better suited for Computer Science, but I have recently gotten interested in problems having to do with different shapes of tiles sliding around in a grid. For example, what sets of tiles are able to be freely slid into all other configurations of those tiles? What shapes of tiles would be able to maneuver anywhere inside a given "arena"? Etc.

Has anyone studied this? If so, please point me to how I can learn more.

Answer 1

Perhaps you may search the Mathematical Subject Classification database.

The search for the keyword tiling in AMS Mathscinet gives a few hits.

05-XX           Combinatorics {For finite fields, see 11Txx}
05Bxx       Designs and configurations {For applications of design theory, see 94C30}
05B45   Combinatorial aspects of tessellation and tiling problems [See also 52C20, 52C22]
37-XX           Dynamical systems and ergodic theory [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX]
37Bxx       Topological dynamics
37B52   Tiling dynamics
52-XX           Convex and discrete geometry
52Cxx       Discrete geometry
52C20   Tilings in $2$ dimensions (aspects of discrete geometry) [See also 05B45, 51M20]
52C22   Tilings in $n$ dimensions (aspects of discrete geometry) [See also 05B45, 51M20]
52C23   Quasicrystals and aperiodic tilings in discrete geometry