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We investigate decomposable combinatorial labeled structures more fully,focusing on the exp-log class of type a=1 or 1/2. For instance, the modallength of the second longest cycle in a random n-permutation is (0.2350...)n,whereas the modal length of the second smallest component in a random n-mappingis 2 (conjecturally, given n>=434). As in earlier work, our approach is toestablish how well existing theory matches experimental data and to raise openquestions.

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