کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6425816 1633843 2013 33 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Triangulations of Cayley and Tutte polytopes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Triangulations of Cayley and Tutte polytopes
چکیده انگلیسی

Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend this result to two one-variable deformations of Cayley polytopes (which we call t-Cayley and t-Gayley polytopes), and to the most general two-variable deformations, which we call Tutte polytopes. The volume of the latter is given via an evaluation of the Tutte polynomial of the complete graph.Our approach is based on an explicit triangulation of the Cayley and Tutte polytopes. We prove that simplices in the triangulations correspond to labeled trees. The heart of the proof is a direct bijection based on the neighbors-first search graph traversal algorithm.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 245, 1 October 2013, Pages 1-33
نویسندگان
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