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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
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
Journal: Advances in Mathematics - Volume 190, Issue 2, 30 January 2005, Pages 319-342
نویسندگان
Lauren K. Williams,