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N. Duong, M. Idan (, Discrete Mathematics Letters)This note addresses hyper-plane arrangements in Rd and functions that are constant in the interior of each of the d-dimensional faces of the arrangement. We show that such a function g can be expressed in a simple form using basis functions that are products of d or less indicator functions of the open half-spaces bounded by the hyper-planes in the arrangement. Moreover, we present a simple and efficient algorithm that can be used to express g as a linear combination of these basis functions.more » « less
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