  The odd diagram of a permutation is a subset of the classical diagram with
additional parity conditions. In this paper, we study classes of permutations
with the same odd diagram, which we call odd diagram classes. First, we prove a
conjecture relating odd diagram classes and 213- and 312-avoiding permutations.
Secondly, we show that each odd diagram class is a Bruhat interval.
Instrumental to our proofs is an explicit description of the Bruhat edges that
link permutations in a class.
