Polynomials with two values

Abstract

This paper investigates the minimal degree of polynomialsfR[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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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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Mathematics Subject Classification (1991):

  • 68R05
  • 11B83
  • 11Y50
  • 11B39