کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4647567 | 1342359 | 2013 | 9 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Rotation number of a unimodular cycle: An elementary approach
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
We give an elementary proof of a formula expressing the rotation number of a cyclic unimodular sequence L=u1u2â¦ud of lattice vectors uiâZ2 in terms of arithmetically defined local quantities. The formula has been originally derived by A. Higashitani and M. Masuda [A. Higashitani, M. Masuda, Lattice multi-polygons, arXiv:1204.0088v2  [math.CO], [v2] Apr 2012; [v3] Dec 2012] with the aid of the Riemann-Roch formula applied in the context of toric topology. These authors also demonstrated that a generalized version of the 'Twelve-point theorem' and a generalized Pick's formula are among the consequences or relatives of their result. Our approach emphasizes the role of 'discrete curvature invariants' μ(a,b,c), where {a,b} and {b,c} are bases of Z2, as fundamental discrete invariants of modular lattice geometry.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 313, Issue 20, 28 October 2013, Pages 2253-2261
Journal: Discrete Mathematics - Volume 313, Issue 20, 28 October 2013, Pages 2253-2261
نویسندگان
Rade T. ŽivaljeviÄ,