Osaka Journal of Mathematics

The rotation number of primitive vector sequences

Yusuke Suyama

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We give a formula on the rotation number of a sequence of primitive vectors, which is a generalization of the formula on the rotation number of a unimodular sequence in [2].

Article information

Osaka J. Math., Volume 52, Number 3 (2015), 849-861.

First available in Project Euclid: 17 July 2015

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Zentralblatt MATH identifier

Primary: 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 57R91: Equivariant algebraic topology of manifolds


Suyama, Yusuke. The rotation number of primitive vector sequences. Osaka J. Math. 52 (2015), no. 3, 849--861.

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  • W. Fulton: Introduction to Toric Varieties, Annals of Mathematics Studies 131, Princeton Univ. Press, Princeton, NJ, 1993.
  • A. Higashitani and M. Masuda: Lattice multi-polygons, arXiv:1204.0088v3.
  • R.T. Živaljević: Rotation number of a unimodular cycle: an elementary approach, arXiv: 1209.4981v4, to appear in Discrete Math.
  • M. Masuda: Unitary toric manifolds, multi-fans and equivariant index, Tohoku Math. J. (2) 51 (1999), 237–265.
  • A.M. Kasprzyk and B. Nill: Reflexive polytopes of higher index and the number 12, Electron. J. Combin. 19 (2012).