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Polynomials with two values

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Abstract

This paper investigates the minimal degree of polynomialsf∈R[x] that take exactly two values on a given range of integers {0,...n}. We show that thegap, defined asn-deg(f), isO(n 548). The maximal gap forn≤128 is 3. As an application, we obtain a bound on the Fourier degree of symmetric Boolean functions.

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Authors and Affiliations

  1. FB Mathematik-Informatik, Universität-GH Paderborn, D-33095, Paderborn, Germany

    Joachim von Zur Gathen

  2. Center for Communications Research, Thanet Road, 08540, Princeton, NJ, USA

    James R. Roche

Authors
  1. Joachim von Zur Gathen
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  2. James R. Roche
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von Zur Gathen, J., Roche, J.R. Polynomials with two values. Combinatorica 17, 345–362 (1997). https://doi.org/10.1007/BF01215917

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  • DOI: https://doi.org/10.1007/BF01215917

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