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arXiv · 1707.02871

How to cut a cake with a gram matrix

Guillaume Chèze·Luca Amodei
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Abstract

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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Guillaume Chèze, Luca Amodei. 2017-07-07. How to cut a cake with a gram matrix. https://arxiv.org/abs/1707.02871

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