کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903619 | 1632747 | 2018 | 37 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On groups and simplicial complexes
ترجمه فارسی عنوان
در گروه ها و مجتمع های ساده
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
The theory of k-regular graphs is closely related to group theory. Every k-regular, bipartite graph is a Schreier graph with respect to some group G, a set of generators S (depending only on k) and a subgroup H. The goal of this paper is to begin to develop such a framework for k-regular simplicial complexes of general dimension d. Our approach does not directly generalize the concept of a Schreier graph, but still presents an extensive family of k-regular simplicial complexes as quotients of one universal object: the k-regular d-dimensional arboreal complex, which is itself a simplicial complex originating in one specific group depending only on d and k. Along the way we answer a question from Parzanchevski and Rosenthal (2016) on the spectral gap of higher dimensional Laplacians and prove a high dimensional analogue of Leighton's graph covering theorem. This approach also suggests a random model for k-regular d-dimensional multicomplexes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: European Journal of Combinatorics - Volume 70, May 2018, Pages 408-444
Journal: European Journal of Combinatorics - Volume 70, May 2018, Pages 408-444
نویسندگان
Alexander Lubotzky, Zur Luria, Ron Rosenthal,