A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired sizes and divide the cake among the groups, so that each group receives a single contiguous piece and no player finds the piece of another group better than that of the player's own group.

中文翻译：

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如何公平地切蛋糕：对群体的概括

切蛋糕的一个基本结果表明，对于对蛋糕有任意偏好的任意数量的玩家，存在蛋糕的分割，使得每个玩家都收到一个连续的一块，并且没有玩家会嫉妒。我们通过展示可以将玩家分成任何所需大小的组并将蛋糕分给各组来概括这个结果，这样每个组都会收到一个连续的棋子，并且没有玩家找到比另一组更好的棋子玩家自己的组。