A generalization of G-parking functions

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The classical parking functions are defined as follows.There are n parking spaces which are arranged in a line, numbered 0 to n-1 left to right and n drivers labeled 1,…,n.Each driver i has an initial parking preference ai.Drivers enter the parking area in the order in which they are labeled.Each driver proceeds to his preferred space and parks here if it is free, or parks at the next unoccupied space to the right.If all the drivers park successfully by this rule, then the sequence (a1,…, an) is called a parking function.
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