کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4584064 1630472 2015 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conway–Coxeter friezes and beyond: Polynomially weighted walks around dissected polygons and generalized frieze patterns
ترجمه فارسی عنوان
فاکس کوئستر کنویا و فراتر از آن: چند ضلعی محض چند ضلعی محض و الگوهای فرعی تعمیم یافته
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

Conway and Coxeter introduced frieze patterns in 1973 and classified them via triangulated polygons. The determinant of the matrix associated to a frieze table was computed explicitly by Broline, Crowe and Isaacs in 1974, a result generalized 2012 by Baur and Marsh in the context of cluster algebras of type A. Higher angulations of polygons and associated generalized frieze patterns were studied in a joint paper with Holm and Jørgensen. Here we take these results further; we allow arbitrary dissections and introduce polynomially weighted walks around such dissected polygons. The corresponding generalized frieze table satisfies a complementary symmetry condition; its determinant is a multisymmetric multivariate polynomial that is given explicitly. But even more, the frieze matrix may be transformed over a ring of Laurent polynomials to a nice diagonal form generalizing the Smith normal form result given in [3]. Considering the generalized polynomial frieze in this context it is also shown that the non-zero local determinants are monomials that are given explicitly, depending on the geometry of the dissected polygon.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 442, 15 November 2015, Pages 80–103
نویسندگان
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