کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6424037 | 1632767 | 2016 | 16 صفحه PDF | دانلود رایگان |
Generalized associahedra were introduced by S. Fomin and A. Zelevinsky in connection to finite type cluster algebras. Following recent work of L. Pournin in types A and B, this paper focuses on geodesic properties of generalized associahedra. We prove that the graph diameter of the n-dimensional associahedron of type D is precisely 2nâ2 for all n greater than 1. Furthermore, we show that all type BCD associahedra have the non-leaving-face property, that is, any geodesic connecting two vertices in the graph of the polytope stays in the minimal face containing both. This property was already proven by D. Sleator, R. Tarjan and W. Thurston for associahedra of type A. In contrast, we present relevant examples related to the associahedron that do not always satisfy this property.
Journal: European Journal of Combinatorics - Volume 51, January 2016, Pages 109-124