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The odd diagram of a permutation is a subset of the classical diagram withadditional parity conditions. In this paper, we study classes of permutationswith the same odd diagram, which we call odd diagram classes. First, we prove aconjecture 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 thatlink permutations in a class.

Odd diagrams, Bruhat order, and pattern avoidance