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Loehr and Warrington introduced partitional statistics$\mbox{ctot}_{\frac{q}{p}}(D)$ and $\mbox{midd}_{\frac{q}{p}}(D)$ and providedformulas for these statistics in terms of the boundary graph of the Youngdiagram $D$. In this paper we give a bijective proof of Loehr-Warrington'sformulas using the following simple combinatorial observation: given a Youngdiagram $D$ and two numbers $a$ and $l,$ the number of boxes in $D$ with thearm length $a$ and the leg length $l$ is one less than the number of boxes withthe same properties in the complement to $D.$ Here the complement is takeninside the positive quadrant or, equivalently, a very large rectangle.

A bijective proof of Loehr-Warrington's formulas for the statistics $\mbox{ctot}_{\frac{q}{p}}$ and $\mbox{midd}_{\frac{q}{p}}$