The joint distribution of the leading-elements and level-set-size statistics on parking functions is derived exactly, and both statistics are shown via breadth-first search to be tree-degree statistics, giving bijective explanations of their equidistribution.
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Distribution of new statistics of parking functions and their generalizations
The joint distribution of the leading-elements and level-set-size statistics on parking functions is derived exactly, and both statistics are shown via breadth-first search to be tree-degree statistics, giving bijective explanations of their equidistribution.