کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4648896 | 1342435 | 2010 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On well-rounded sublattices of the hexagonal lattice
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
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چکیده انگلیسی
We produce an explicit parameterization of well-rounded sublattices of the hexagonal lattice in the plane, splitting them into similarity classes. We use this parameterization to study the number, the greatest minimal norm, and the highest signal-to-noise ratio of well-rounded sublattices of the hexagonal lattice of a fixed index. This investigation parallels earlier work by Bernstein, Sloane, and Wright where similar questions were addressed on the space of all sublattices of the hexagonal lattice. Our restriction is motivated by the importance of well-rounded lattices for discrete optimization problems. Finally, we also discuss the existence of a natural combinatorial structure on the set of similarity classes of well-rounded sublattices of the hexagonal lattice, induced by the action of a certain matrix monoid.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 310, Issue 23, 6 December 2010, Pages 3287-3302
Journal: Discrete Mathematics - Volume 310, Issue 23, 6 December 2010, Pages 3287-3302
نویسندگان
Lenny Fukshansky, Daniel Moore, R. Andrew Ohana, Whitney Zeldow,