Abstract:

We will consider the set of twisted involutions of a Coxeter group with the order relation induced by the Bruhat order. The twisted involutions with Boolean lower order ideals are classified via their reduced expressions. As a special case we will classify the involutions in the symmetric group with Boolean lower order ideals. The classification will also be given via permutation patterns. We will count these involutions by some statistics and deduce a bijective correspondence to certain Motzkin paths.