Pascal's Triangle and Its Relatives

Exercises

Pascal's triangles of some finite groups

4. Here are the Pascal's triangles for D3. with b along the left side and d along the right side. We shade the boxes containing

left and rightb, d b, db, eb, f
shading a,b,c d,e,f d,e,f d,e,f

Note a rotation and any of the reflections generates the same pattern.

Here are larger and larger Pascal's triangles, with c on the left and f on the right, shading the boxes containing b, c, d, or e. Vote this resembles a Class 4 automaton. Click the lest three to enlarge in new windows.

Return to Finite groups Exercises.