“Cake Cutting”的概念、定义、习题解题方法及翻译-数学辞典

单词

Cake Cutting

释义

Cake Cutting

It is always possible to ``fairly'' divide a cake among people using only vertical cuts. Furthermore, it is possible tocut and divide a cake such that each person believes that everyone has received of the cake according to his ownmeasure. Finally, if there is some piece on which two people disagree, then there is a way of partitioning and dividing acake such that each participant believes that he has obtained more than of the cake according to his own measure.

Ignoring the height of the cake, the cake-cutting problem is really a question of fairly dividing a Circle into equalArea pieces using cuts in its plane. One method of proving fair cake cutting to always be possible relies on theFrobenius-König Theorem.

See also Circle Cutting, Cylinder Cutting, Envyfree, Frobenius-König Theorem, Ham Sandwich Theorem, PancakeTheorem, Pizza Theorem, Square Cutting, Torus Cutting

References

Brams, S. J. and Taylor, A. D. ``An Envy-Free Cake Division Protocol.'' Amer. Math. Monthly 102, 9-19, 1995.

Brams, S. J. and Taylor, A. D. Fair Division: From Cake-Cutting to Dispute Resolution. New York: Cambridge University Press, 1996.

Dubbins, L. and Spanier, E. ``How to Cut a Cake Fairly.'' Amer. Math. Monthly 68, 1-17, 1961.

Gale, D. ``Dividing a Cake.'' Math. Intel. 15, 50, 1993.

Jones, M. L. ``A Note on a Cake Cutting Algorithm of Banach and Knaster.'' Amer. Math. Monthly 104, 353-355, 1997.

Rebman, K. ``How to Get (At Least) a Fair Share of the Cake.'' In Mathematical Plums (Ed. R. Honsberger). Washington, DC: Math. Assoc. Amer., pp. 22-37, 1979.

Steinhaus, H. ``Sur la division pragmatique.'' Ekonometrika (Supp.) 17, 315-319, 1949.

Stromquist, W. ``How to Cut a Cake Fairly.'' Amer. Math. Monthly 87, 640-644, 1980.

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