A moving-knife solution to the four-person envy-free cake-division problem
HTML articles powered by AMS MathViewer
- by Steven J. Brams, Alan D. Taylor and William S. Zwicker PDF
- Proc. Amer. Math. Soc. 125 (1997), 547-554 Request permission
Abstract:
We present a moving-knife procedure, requiring only 11 cuts, that produces an envy-free allocation of a cake among four players and discuss possible extensions to five players.References
- A. K. Austin, “Sharing a cake”, Mathematical Gazette 6, no. 437 (October 1982), 212–215.
- S. J. Brams and A. D. Taylor, “An envy-free cake-division protocol”, American Mathematical Monthly 102, no. 1 (January 1995), 9–18.
- S. J. Brams and A. D. Taylor, Fair Division: From Cake-Cutting to Dispute Resolution, Cambridge, UK: Cambridge University Press (1996).
- Steven J. Brams and Alan D. Taylor, On envy-free cake division, J. Combin. Theory Ser. A 70 (1995), no. 1, 170–173. MR 1324009, DOI 10.1016/0097-3165(95)90088-8
- S. J. Brams, A. D. Taylor, and W. S. Zwicker, “Old and new moving-knife schemes”, Mathematical Intelligencer 17, no. 4 (Fall, 1995).
- P. Erdös and T. Grünwald, On polynomials with only real roots, Ann. of Math. (2) 40 (1939), 537–548. MR 7, DOI 10.2307/1968938
- H. Steinhaus, “The problem of fair division”, Econometrica 16, no. 1 (January 1948), 101–104.
- Walter Stromquist, How to cut a cake fairly, Amer. Math. Monthly 87 (1980), no. 8, 640–644. MR 600922, DOI 10.2307/2320951
- W. Webb, “But he got a bigger piece than I did”, preprint, n.d.
Additional Information
- Steven J. Brams
- Affiliation: Department of Politics, New York University, New York, New York 10003
- Email: brams@is2.nyu.edu
- Alan D. Taylor
- Affiliation: Department of Mathematics, Union College, Schenectady, New York 12308
- Email: taylora@gar.union.edu
- William S. Zwicker
- Email: zwickerw@gar.union.edu
- Received by editor(s): December 20, 1994
- Received by editor(s) in revised form: August 29, 1995
- Communicated by: Andreas R. Blass
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 547-554
- MSC (1991): Primary 90D10; Secondary 62C20
- DOI: https://doi.org/10.1090/S0002-9939-97-03614-9
- MathSciNet review: 1353378