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Arc permutations, which were originally introduced in the study of triangulations and characters, have recently been shown to have interesting combinatorial properties. The first part of this paper continues their study by providing signed enumeration formulas with respect to their descent set and major index. Next, we generalize the notion of arc permutations to the hyperoctahedral group in two different directions. We show that these extensions to type B carry interesting analogues of thedoi:10.4310/joc.2015.v6.n1.a11 fatcat:hbdz622rqjabjmmumkl4n4y5hi