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Lett. {\\bf 105}, 246808 (2010)] offers a clue into the physical mechanism of the FQHE in the second Landau level (SLL). Here we propose a \"$\\bar{3}\\bar{2}111$\" parton wave function, which is topologically distinct from the 6/13 state in the lowest Landau level. We demonstrate the $\\bar{3}\\bar{2}111$ state to be a good candidate for the $\\nu=2+6/13$ FQHE, and make predictions for experimentally measurable properties that can reveal the nature of this state. 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