Josuat-Verg 在NC(W) 中給出了一個Deligne formula 的q-analogue ，其中標記的weighted我們稱之為爛邊，即此邊連接的兩個元素在strong bruhat order 和absolute order 中的大小關係剛好相反。接著我們已知Type A 的absolute order of maximal chains 的數量恰恰好是parking function 個，於是我們想在parking function 上找到和爛邊等分布的統計量。而此篇論文我們不只找到等分布的統計量(將就) ，還有給出保持統計量的bijecton 並進一步做出Type B 版本，以及給出Type B 的q-analogue 中gamma-positivity 係數的組合意義。

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