Parametrization for stationary patterns of the r-majority operators on 0-1 sequences

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For a nonnegative integer p and a two-way infinite sequence u=(um)m∈Z of complex numbers define the sequence v = Apu by vm=(Apu)m= ∑ -p≤j≤p(-1)p+jum+j (m∈Z). The spaces Up and Vp of the sequences u fixed by A2p and Ap are studied, and given several parametrizations. These spaces play a fundamental role in the description of two-way-infinite 0-1 sequences that reoccur - and, in particular, that are fixed - by the r-majority operators M. M simultaneously replaces every bit of a two-way-infinite 0-1 sequence by the majority bit of the (2r + 1)-segment it centers [2, 9].

Original languageEnglish
Pages (from-to)175-195
Number of pages21
JournalDiscrete Mathematics
Issue number1-3
StatePublished - 15 Sep 1994


  • 0-1 sequences
  • Cellular automata
  • Majority rule
  • Stationary states

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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