کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
10327451 | 681073 | 2005 | 16 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The affine representation theorem for abstract convex geometries
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The affine representation theorem for abstract convex geometries The affine representation theorem for abstract convex geometries](/preview/png/10327451.png)
چکیده انگلیسی
A convex geometry is a combinatorial abstract model introduced by Edelman and Jamison which captures a combinatorial essence of “convexity” shared by some objects including finite point sets, partially ordered sets, trees, rooted graphs. In this paper, we introduce a generalized convex shelling, and show that every convex geometry can be represented as a generalized convex shelling. This is “the representation theorem for convex geometries” analogous to “the representation theorem for oriented matroids” by Folkman and Lawrence. An important feature is that our representation theorem is affine-geometric while that for oriented matroids is topological. Thus our representation theorem indicates the intrinsic simplicity of convex geometries, and opens a new research direction in the theory of convex geometries.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Geometry - Volume 30, Issue 2, February 2005, Pages 129-144
Journal: Computational Geometry - Volume 30, Issue 2, February 2005, Pages 129-144
نویسندگان
Kenji Kashiwabara, Masataka Nakamura, Yoshio Okamoto,