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  1. (, Acta mathematica Universitatis Comenianae)
    Pop-stack sorting is an important variation for sorting permutations via a stack. A single iteration of pop-stack sorting is the transformation T : S_n -> S_n that reverses all the maximal descending sequences of letters in a permutation. We investigate structural and enumerative aspects of pop-stacked permutations – the permutations that belong to the image of Sn under T. This work is part of a project aiming to provide the full combinatorial analysis of sorting with a pop-stack, as it was successfully done for sorting with a stack (though, even in this case, some famous problems are still open). The first results already show that pop-stack sorting has a very rich combinatorial structure, and leads to surprising phenomena. 
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