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We study the partial orders induced on Wachs and signed Wachs permutations bythe Bruhat and weak orders of the symmetric and hyperoctahedral groups. We showthat these orders are graded, determine their rank function, characterize theirordering and covering relations, and compute their characteristic polynomials,when partially ordered by Bruhat order, and determine their structureexplicitly when partially ordered by right weak order.

Wachs permutations, Bruhat order and weak order