# Analysis of the Gift Exchange Problem

@article{Apagodu2017AnalysisOT, title={Analysis of the Gift Exchange Problem}, author={Moa Apagodu and David L. Applegate and N. J. A. Sloane and Doron Zeilberger}, journal={Electron. J. Comb.}, year={2017}, volume={24}, pages={3} }

In the gift exchange game there are $n$ players and $n$ wrapped gifts. When a player's number is called, that person can either choose one of the remaining wrapped gifts, or can "steal" a gift from someone who has already unwrapped it, subject to the restriction that no gift can be stolen more than a total of $\sigma$ times. The problem is to determine the number of ways that the game can be played out, for given values of $\sigma$ and $n$. Formulas and asymptotic expansions are given for these…

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