Mappings and inductive invariants
Calvin F. K. Jung (1973)
Colloquium Mathematicae
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Calvin F. K. Jung (1973)
Colloquium Mathematicae
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Nguyen To Nhu (1979)
Colloquium Mathematicae
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Albert A. Cuoco (1982)
Mathematische Zeitschrift
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Paul Monsky (1981)
Mathematische Annalen
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Akira Aiba (2003)
Acta Arithmetica
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Marek Karaś (2008)
Bulletin of the Polish Academy of Sciences. Mathematics
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Hans-Georg Rück (1986)
Mathematische Zeitschrift
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Paul Monsky (1986)
Mathematische Zeitschrift
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Kulish, P.P., Nikitin, A.M. (2000)
Zapiski Nauchnykh Seminarov POMI
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A. Błaszczyk, U. Lorek (1978)
Colloquium Mathematicae
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Paweł Szeptycki (1975)
Studia Mathematica
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T. K. Pal, M. Maiti, J. Achari (1976)
Matematički Vesnik
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D. W. Hajek (1986)
Matematički Vesnik
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Yuka Kotorii (2014)
Fundamenta Mathematicae
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We define finite type invariants for cyclic equivalence classes of nanophrases and construct universal invariants. Also, we identify the universal finite type invariant of degree 1 essentially with the linking matrix. It is known that extended Arnold basic invariants to signed words are finite type invariants of degree 2, by Fujiwara's work. We give another proof of this result and show that those invariants do not provide the universal one of degree 2.