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.
Domains
Information Theory [cs.IT]
Origin : Files produced by the author(s)
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