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A106797
Fixed point of the morphism 1 -> 1,1,1,1,2,2,3; 2 -> 4,1; 3 -> 2,1,1,1; 4 -> 1,2,1 starting with a(0) = 1.
4
1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 4, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 4, 1, 4, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 2, 2, 3, 4, 1, 4, 1, 2
OFFSET
0,5
COMMENTS
4-symbol substitution of the Pisot characteristic polynomial: x^4 - 4*x^3 - 6*x^2 - x - 1.
LINKS
Victor F. Sirvent and Boris Solomyak, Pure Discrete Spectrum for One-dimensional Substitution Systems of Pisot Type. Canadian Mathematical Bulletin, 45(4), 2002, 697-710; (page 709 example 4). Also at ResearchGate
EXAMPLE
The first few steps of the substitution are:
Start: 1
Maps:
1 --> 1 1 1 1 2 2 3
2 --> 4 1
3 --> 2 1 1 1
4 --> 1 2 1
-------------
0: (#=1)
1
1: (#=7)
1111223
2: (#=36)
111122311112231111223111122341412111
MATHEMATICA
s[1]= {1, 1, 1, 1, 2, 2, 3}; s[2]= {4, 1}; s[3]= {2, 1, 1, 1}; s[4]= {1, 2, 1};
t[a_]:= Flatten[s /@ a]; p[0]= {1}; p[1]= t[p[0]]; p[n_]:= t[p[n-1]]; p[3]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, May 17 2005
EXTENSIONS
Edited by G. C. Greubel, Apr 03 2022
STATUS
approved