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Related Links (Outside this Site)

Francis Su's Fair Division Page.

"An Envy-Free Cake Division Protocol" Steven J. Brams & Alan D. Taylor
The American Mathematical Monthly, 102, 1, pp. 9-18, (January 1995).

Wikipedia : Fair division | Entitlement

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(2017年02月24日) Sperner's Lemma (Emanuel Sperner, 1928)
The number of full-color simplices in a Sperner triangulation is odd.

Sperner's lemma is the combinatorial equivalent of Brouwer's fixed-point theorem.

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Rental Harmony: Sperner's Lemma in Fair Division by Francis Edward Su.
American Mathematical Monthly, 106 (1999) pp. 930-942.

To Divide the Rent, Start With a Triangle by Albert Sun (New-York Times, 2014年04月28日)

Sperner's lemma defeats the rental harmony problem (15:34) by Burkard Polster (Mathologer, 2017年02月10日).
Splitting Rent with Triangles (16:20) by Kelsey Houston-Edwards (PBS Infinite Series, 2017年02月23日).
Proving Brouwer's fixed-point theorem with Sperner's lemma (19:29) by Trefor Bazett (2018年03月11日).

Wikipedia : Sperner's lemma (1928) | Emanuel Sperner (1905-1980)

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(2017年02月24日) Stolen Necklace Problem
With N different types of beads, N cuts are enough for a fair split.

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Borsuk-Ulam Theorem (21:54) by Grant Sanderson (3Blue1Brown, 2017年02月10日).
Borsuk-Ulam Theorem (16:36) by Trefor Bazett (2018年12月16日).

Wikipedia : Borsuk-Ulam Theorem | Karol Borsuk (1905-1982) | Stanislaw Ulam (1909-1984)