کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4654475 1632845 2006 15 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The positive Bergman complex of an oriented matroid
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
The positive Bergman complex of an oriented matroid
چکیده انگلیسی

We study the positive Bergman complex B+(M)B+(M) of an oriented matroid MM, which is a certain subcomplex of the Bergman complex B(M¯) of the underlying unoriented matroid M¯. The positive Bergman complex is defined so that given a linear ideal II with associated oriented matroid MIMI, the positive tropical variety associated with II is equal to the fan over B+(MI)B+(MI). Our main result is that a certain “fine” subdivision of B+(M)B+(M) is a geometric realization of the order complex of the proper part of the Las Vergnas face lattice of MM. It follows that B+(M)B+(M) is homeomorphic to a sphere. For the oriented matroid of the complete graph KnKn, we show that the face poset of the “coarse” subdivision of B+(Kn)B+(Kn) is dual to the face poset of the associahedron An−2An−2, and we give a formula for the number of fine cells within a coarse cell.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 27, Issue 4, May 2006, Pages 577–591
نویسندگان
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