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A Generalization of Montucla's Rectangle-to-Rectangle Dissection to Higher Dimensions

Abstract : Dissections of polytopes are a well-studied subject by ge-ometers as well as recreational mathematicians. A recent application in coding theory arises from the problem of parameterizing binary vectors of constant Hamming weight [TVS09], [SV09], which is shown to be equivalent to the problem of dissecting a tetrahedron to a brick. An application of dissections to a problem related to the construction of analog codes arises in [CVC13]. Here we consider the rectangle-to-rectangle dissection due to Montu-cla [Fre03]. Montucla's dissection is first reinterpreted in terms of the Two Tile Theorem [SV09]. Based on this, a cube-to-brick dissection is developed in R^n. We present a linear time algorithm (in n) that computes the dissection, i.e. determines a point in the cube given a point in a specific realization of the brick. An application of this algorithm to a previously reported analog coding scheme [CVC13] is also discussed.
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https://hal.inria.fr/hal-01276485
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Submitted on : Friday, February 19, 2016 - 2:37:11 PM
Last modification on : Tuesday, August 13, 2019 - 1:42:01 PM
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Antonio Campello, Vinay Vaishampayan. A Generalization of Montucla's Rectangle-to-Rectangle Dissection to Higher Dimensions. The 9th International Workshop on Coding and Cryptography 2015 WCC2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01276485⟩

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