Abstract
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 language | English |
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Pages (from-to) | 175-195 |
Number of pages | 21 |
Journal | Discrete Mathematics |
Volume | 132 |
Issue number | 1-3 |
DOIs | |
State | Published - 15 Sep 1994 |
Keywords
- 0-1 sequences
- Cellular automata
- Majority rule
- Stationary states
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics