Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

Binary Sequences which Contain no $BBb$

Earl D. Fife
Transactions of the American Mathematical Society
Vol. 261, No. 1 (Sep., 1980), pp. 115-136
DOI: 10.2307/1998321
Stable URL: http://www.jstor.org/stable/1998321
Page Count: 22
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Binary Sequences which Contain no $BBb$
Preview not available

Abstract

A (one-sided) sequence or (two-sided) bisequence is irreducible provided it contains no block of the form $BBb$, where $b$ is the initial symbol of the block $B$. Gottschalk and Hedlund [Proc. Amer. Math. Soc. 15 (1964), 70-74] proved that the set of irreducible binary bisequences is the Morse minimal set $M$. Let $M^+$ denote the one-sided Morse minimal set, i.e. $M^+ = \{x_0x_1x_2 \ldots:\ldots x_{-1}x_0x_1 \ldots \in M\}$. Let $P^+$ denote the set of all irreducible binary sequences. We establish a method for generating all $x \in P^+$. We also determine $P^+ - M^+$. Considering $P^+$ as a one-sided symbolic flow, $P^+$ is not the countable union of transitive flows, thus $P^+$ is considerably larger than $M^+$. However $M^+$ is the $\omega$-limit set of each $x \in P^+$, and in particular $M^+$ is the nonwandering set of $P^+$.

Page Thumbnails

  • Thumbnail: Page 
115
    115
  • Thumbnail: Page 
116
    116
  • Thumbnail: Page 
117
    117
  • Thumbnail: Page 
118
    118
  • Thumbnail: Page 
119
    119
  • Thumbnail: Page 
120
    120
  • Thumbnail: Page 
121
    121
  • Thumbnail: Page 
122
    122
  • Thumbnail: Page 
123
    123
  • Thumbnail: Page 
124
    124
  • Thumbnail: Page 
125
    125
  • Thumbnail: Page 
126
    126
  • Thumbnail: Page 
127
    127
  • Thumbnail: Page 
128
    128
  • Thumbnail: Page 
129
    129
  • Thumbnail: Page 
130
    130
  • Thumbnail: Page 
131
    131
  • Thumbnail: Page 
132
    132
  • Thumbnail: Page 
133
    133
  • Thumbnail: Page 
134
    134
  • Thumbnail: Page 
135
    135
  • Thumbnail: Page 
136
    136