M. Morse and G. A. Hedlund. Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J., 11:1--7, 1944. Home/Search Document Not in Database Summary Related Articles Check |
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A Characterization of .. -free Words over a Binary Alphabet - Lepisto (Correct)
....been many papers about this topic. In this work we are going to deal with a specific pattern. An alphabet is a finite set. A word over some alphabet is a sequence of elements (called symbols or letters) of this alphabet (cf. Lo] and [CK] It was proved by Thue (and independently by Morse (cf. [MH]) that the Thue Morse sequence, which is obtained by the Thue Morse morphism, is an infinite word over binary alphabet which does not contain any subwords of the form uvuvu, where u is a symbol from that alphabet and v is an arbitrary word over the same alphabet. Therefore, the pattern uvuvu is ....
M. Morse and G.A. Hedlund: Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J. 11 (1944) 1-7.
Extremal Infinite Overlap-Free Binary Words - Allouche, Currie (1997) (Correct)
....to an overlap free doubly infinite sequence, since the prefix 00100 is forbidden from the claim above. Hence such a sequence must begin with 00101, hence with 0010110. On the other hand, it is well known that t is extendable to the left to a doubly infinite overlap free sequence ( 15, Satz 7] [12], 5, p. 30] 5 The lexicographically least square free sequence As already proved by Thue, it is possible to construct, on a three letter alphabet, a sequence without squares, i.e. without any factor of the form ww,wherewis a nonempty word. It is readily checked that there is no square free ....
M. Morse and G. A. Hedlund, Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11 (1944), 1-7.
Extremal Infinite Overlap-Free Binary Words - Allouche, Currie (1997) (Correct)
....to an overlap free doubly infinite sequence, since the prefix 00100 is forbidden from the claim above. Hence such a sequence must begin with 00101, hence with 0010110. On the other hand, it is well known that t is extendable to the left to a doubly infinite overlap free sequence ( 15, Satz 7] [12], 5, p. 30] 5 The lexicographically least square free sequence As already proved by Thue, it is possible to construct, on a three letter alphabet, a sequence without squares, i.e. without any factor of the form ww, where w is a nonempty word. It is readily checked that there is no ....
M. Morse and G. A. Hedlund, Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11 (1944), 1-7.
Periodicity and Repetition in Combinatorics on Words - Wang (2004) (Correct)
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M. Morse and G. A. Hedlund. Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J., 11:1--7, 1944.
Counting the Occurrences of Generalized Patterns in Words.. - Kitaev, Mansour (2002) (Correct)
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Morse M., Hedlung G.: Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. Journal, Vol. 11, No. 1 (1944), 1-7.
Infinite Sequences and Pattern Avoidance - Rampersad (2004) (Correct)
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M. Morse and G. A. Hedlund. Unending chess, symbolic dynamics and a problem in semigroups. Duke Math. J. 11 (1944), 1--7.
On Abelian Circular Squares in Binary Words - Fraenkel, Simpson, Paterson (Correct)
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M. Morse and G.A. Hedlund [1944], Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11, 1--7.
How Many Squares Must a Binary Sequence Contain? - Fraenkel, Simpson (1994) (Correct)
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M. Morse and G.A. Hedlund [1944], Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11, 1--7.
How Many Squares Must a Binary Sequence Contain? - Fraenkel, Simpson (1995) (Correct)
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M. Morse and G.A. Hedlund [1944], Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11, 1--7.
On Weak Circular Squares in Binary Words - Fraenkel, Simpson, Paterson (Correct)
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M. Morse and G.A. Hedlund [1944], Unending chess, symbolic dynamics and a problem in semigroups, Duke Math. J. 11, 1--7.
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