List of tuples without forbidden pair

Question

How do you get a list of tuples in Mathematica that do not include certain pairs of elements? For example, I'm trying to list sequences of matrices of a certain length, and I do not want two adjacent elements in the sequence to be inverses of each other.

I suspect the code will end up looking like:

DropCases[Tuples[{a, b, Inverse[a], Inverse[a]}, 6], ???]

How do I do this in Mathematica?

Thanks!

Answer 1

CORRECTED per input from RunnyKine

Length[Tuples[{a, b, Inverse[a], Inverse[a]}, 6]]

4096

Length[
 DeleteCases[
  DeleteCases[Tuples[{a, b, Inverse[a], Inverse[a]}, 6],
   {___, x_, Inverse[x_], ___}],
  {___, Inverse[x_], x_, ___}]]

1204

Length[
 DeleteCases[Tuples[{a, b, Inverse[a], Inverse[a]}, 6],
  {___, x_, Inverse[x_], ___} | {___, Inverse[x_], x_, ___}]]

1204

Answer 2

Is your application time-critical? The first thing that comes into my 3:27-in-the-morning-mind is to make a pattern that tests whether a*b=1 (or with matrices a.b==IdentityMatrix[n]). Here is an example with numbers that should work for your matrices too when you adapt it

DeleteCases[
 Tuples[{1, 2, 1^-1, 2^-1}, 5], {___, x_, y_, ___} /; x*y === 1]

The output looks ok at the first glance.