Odd diagrams, Bruhat order, and pattern avoidance

The odd diagram of a permutation is a subset of the classical diagram with ad-ditional 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.