The shifting method is one of the most powerful tools in extremal set theory, invented by Erdős, Ko and Rado, and further developed by Frankl, Ahlswede and Khachatrian. In this paper, we survey some developments of the shifting method including the random walk method, the generating set method and the recently developed shifting ad extremis by Frankl. To illustrate the power of the shifting method, we review some proofs and proof ideas.

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Developments of the Shifting Method in Extremal Set Theory

  • Jian Wang

摘要

The shifting method is one of the most powerful tools in extremal set theory, invented by Erdős, Ko and Rado, and further developed by Frankl, Ahlswede and Khachatrian. In this paper, we survey some developments of the shifting method including the random walk method, the generating set method and the recently developed shifting ad extremis by Frankl. To illustrate the power of the shifting method, we review some proofs and proof ideas.