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Article Dans Une Revue Linear Algebra and its Applications Année : 2019

How to cut a cake with a gram matrix

Résumé

In this article we study the problem of fair division. In particular we study a notion introduced by J. Barbanel that generalizes super envy-free fair division. We give a new proof of his result. Our approach allows us to give an explicit bound for this kind of fair division. Furthermore, we also give a theoretical answer to an open problem posed by Barbanel in 1996. Roughly speaking, this question is: how can we decide if there exists a fair division satisfying some inequalities constraints? Furthermore, when all the measures are given with piecewise constant density functions then we show how to construct effectively such a fair division.
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hal-01557946 , version 1 (06-07-2017)

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Guillaume Chèze, Luca Amodei. How to cut a cake with a gram matrix. Linear Algebra and its Applications, 2019, 560. ⟨hal-01557946⟩
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