کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903780 | 1632916 | 2018 | 43 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
COMs: Complexes of oriented matroids
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: COMs: Complexes of oriented matroids COMs: Complexes of oriented matroids](/preview/png/8903780.png)
چکیده انگلیسی
In his seminal 1983 paper, Jim Lawrence introduced lopsided sets and featured them as asymmetric counterparts of oriented matroids, both sharing the key property of strong elimination. Moreover, symmetry of faces holds in both structures as well as in the so-called affine oriented matroids. These two fundamental properties (formulated for covectors) together lead to the natural notion of “conditional oriented matroid” (abbreviated COM). These novel structures can be characterized in terms of three cocircuits axioms, generalizing the familiar characterization for oriented matroids. We describe a binary composition scheme by which every COM can successively be erected as a certain complex of oriented matroids, in essentially the same way as a lopsided set can be glued together from its maximal hypercube faces. A realizable COM is represented by a hyperplane arrangement restricted to an open convex set. Among these are the examples formed by linear extensions of ordered sets, generalizing the oriented matroids corresponding to the permutohedra. Relaxing realizability to local realizability, we capture a wider class of combinatorial objects: we show that non-positively curved Coxeter zonotopal complexes give rise to locally realizable COMs.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 156, May 2018, Pages 195-237
Journal: Journal of Combinatorial Theory, Series A - Volume 156, May 2018, Pages 195-237
نویسندگان
Hans-Jürgen Bandelt, Victor Chepoi, Kolja Knauer,