Counterexamples in the theory of fair division

Details Counterexamples in the theory of fair division Counterexamples in the theory of fair division

2009-01-15

arxiv.org/abs/0901.2360v1

Cutting Cakes Carefully, The College Mathematics Journal, 41 (2010) 281-288

Mathematics

Probability

Available at http://digitalcommons.calpoly.edu/rgp_rsr/73/

Scientific paper

The formal mathematical theory of fair division has a rich history dating back at least to Steinhaus in the 1940's. In recent work in this area, several general classes of errors have appeared along with confusion about the necessity and sufficiency of certain hypotheses. It is the purpose of this article to correct the scientific record and to point out with concrete examples some of the pitfalls that have led to these mistakes. These examples may serve as guideposts for future work.

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