A note on hyper-plane arrangements in Rd

Nhattrieu Duong, Moshe Idan, Rom Pinchasi, Jason L. Speyer

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)79-85
Number of pages7
JournalDiscrete Mathematics Letters
StatePublished - 2021


  • Hyperplane-arrangements
  • Hyperplanes
  • Linear basis

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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