کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4656434 1343436 2006 10 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Polygon dissections and some generalizations of cluster complexes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Polygon dissections and some generalizations of cluster complexes
چکیده انگلیسی

Let W be a Weyl group corresponding to the root system An−1 or Bn. We define a simplicial complex in terms of polygon dissections for such a group and any positive integer m. For m=1, is isomorphic to the cluster complex corresponding to W, defined in [S. Fomin, A.V. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math. 158 (2003) 977–1018]. We enumerate the faces of and show that the entries of its h-vector are given by the generalized Narayana numbers , defined in [C.A. Athanasiadis, On a refinement of the generalized Catalan numbers for Weyl groups, Trans. Amer. Math. Soc. 357 (2005) 179–196]. We also prove that for any m⩾1 the complex is shellable and hence Cohen–Macaulay.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series A - Volume 113, Issue 6, August 2006, Pages 1189-1198