کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9518008 1633860 2005 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Enumeration of totally positive Grassmann cells
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Enumeration of totally positive Grassmann cells
چکیده انگلیسی
Postnikov (Webs in totally positive Grassmann cells, in preparation) has given a combinatorially explicit cell decomposition of the totally nonnegative part of a Grassmannian, denoted Grk,n+, and showed that this set of cells is isomorphic as a graded poset to many other interesting graded posets. The main result of our work is an explicit generating function which enumerates the cells in Grk,n+ according to their dimension. As a corollary, we give a new proof that the Euler characteristic of Grk,n+ is 1. Additionally, we use our result to produce a new q-analog of the Eulerian numbers, which interpolates between the Eulerian numbers, the Narayana numbers, and the binomial coefficients.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 190, Issue 2, 30 January 2005, Pages 319-342
نویسندگان
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