کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591859 1335058 2008 29 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Enhanced negative type for finite metric trees
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Enhanced negative type for finite metric trees
چکیده انگلیسی

A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities (1) that encode the best possible quantification of the strictness of the non-trivial 1-negative type inequalities for finite metric trees. These inequalities are sufficiently strong to imply that any given finite metric tree (T,d) must have strict p-negative type for all p in an open interval (1−ζ,1+ζ), where ζ>0 may be chosen so as to depend only upon the unordered distribution of edge weights that determine the path metric d on T. In particular, if the edges of the tree are not weighted, then it follows that ζ depends only upon the number of vertices in the tree.We also give an example of an infinite metric tree that has strict 1-negative type but does not have p-negative type for any p>1. This shows that the maximal p-negative type of a metric space can be strict.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 254, Issue 9, 1 May 2008, Pages 2336-2364