# Fair Division and Generalizations of Sperner- and KKM-type Results

@article{Asada2017FairDA, title={Fair Division and Generalizations of Sperner- and KKM-type Results}, author={Megumi A Asada and Florian Frick and Vivek Pisharody and Maxwell Polevy and David Stoner and Ling Hei Tsang and Zoe Wellner}, journal={SIAM J. Discret. Math.}, year={2017}, volume={32}, pages={591-610} }

We treat problems of fair division, their various interconnections, and their relations to Sperner's lemma and the Knaster--Kuratowski--Mazurkiewicz (KKM) theorem as well as their variants. We prove extensions of Alon's necklace splitting result in certain regimes and relate it to hyperplane mass partitions. We show the existence of fair cake division and rental harmony in the sense of Su even in the absence of full information. Furthermore, we extend Sperner's lemma and the KKM theorem to…

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