کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4598921 1631110 2015 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Convexity of tropical polytopes
ترجمه فارسی عنوان
غشاء چند قطبی گرمسیری
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

We study the relationship between min-plus, max-plus and Euclidean convexity for subsets of RnRn. We introduce a construction which associates to any max-plus convex set with compact projectivisation a canonical matrix called its dominator. The dominator is a Kleene star whose max-plus column space is the min-plus convex hull of the original set. We apply this to show that a set which is any two of (i) a max-plus polytope, (ii) a min-plus polytope and (iii) a Euclidean polytope must also be the third. In particular, these results answer a question of Sergeev, Schneider and Butkovič [16] and show that row spaces of tropical Kleene star matrices are exactly the “polytropes” studied by Joswig and Kulas [13].

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 485, 15 November 2015, Pages 531–544
نویسندگان
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