کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4602327 | 1631167 | 2008 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the divisibility of meet and join matrices
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله

چکیده انگلیسی
Let (P,⩽)=(P,∧,∨) be a lattice, let S={x1,x2,…,xn} be a meet-closed subset of P and let f:P→Z+ be a function. We characterize the matrix divisibility of the join matrix [S]f=[f(xi∨xj)] by the meet matrix (S)f=[f(xi∧xj)] in the ring Zn×n in terms of the usual divisibility in Z, and we present two algorithms for constructing certain classes of meet-closed sets S such that (S)f divides [S]f. As an example we present the lattice-theoretic structure of all meet-closed sets with at most five elements possessing the matrix divisibility property. Finally, we show that our methods solve some open problems in the divisor lattice, concerning the divisibility of GCD and LCM matrices.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 429, Issues 8–9, 16 October 2008, Pages 1929-1943
Journal: Linear Algebra and its Applications - Volume 429, Issues 8–9, 16 October 2008, Pages 1929-1943