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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A moving-knife solution to the four-person envy-free cake-division problem
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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.
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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