Combinatorics / CONCEPT

The reverse third-position construction

The map undoPhi(n,p) is empty for n = 0 and equals 3142 for n = 4. Otherwise, when p starts with two, delete that entry and decrease every remaining value other than one to obtain q. If q is simple, apply Phi(n-1,q), increase all values, and insert one second; if not, delete its third entry and decrease every value other than one, inflate the first entry of the resulting skeleton by 21, increase all values, and insert one second. When p does not start with two, delete its third entry and subtract one from every remaining value to obtain q. If q is simple, increase its values and insert one second. If q = R(n-1), do this to B(n-1) instead. Otherwise delete the second entry of q, standardize above its third value, inflate the first entry by 21, increase all values, and insert one second.