Sperner theory
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Let N"n denote the quotient poset of the Boolean lattice, B"n, under the relation equivalence under rotation. Griggs, Killian, and Savage proved that N"p is a symmetric chain order for prime p. In this paper, we settle the question posed in that paper, namely whether N"n is a symmetric chain order for all n. This paper provides an algorithm that produces a symmetric chain decomposition (or SCD). We accomplish this by modifying bracketing from Greene and Kleitman. This allows us to take appropriate ''middles'' of certain chains from the Greene-Kleitman SCD for B"n. We also prove additional properties of the resulting SCD and show that this settles a related conjecture.