Simplicial intersection chains for an abstract complex
نویسندگان
چکیده
منابع مشابه
The Intersection of a Matroid and a Simplicial Complex
A classical theorem of Edmonds provides a min-max formula relating the maximal size of a set in the intersection of two matroids to a “covering” parameter. We generalize this theorem, replacing one of the matroids by a general simplicial complex. One application is a solution of the case r = 3 of a matroidal version of Ryser’s conjecture. Another is an upper bound on the minimal number of sets ...
متن کاملAbstract Simplicial Complexes
Simplicial Complexes Karol Pąk Institute of Computer Science University of Białystok Poland Summary. In this article we define the notion of abstract simplicial complexes and operations on them. We introduce the following basic notions: simplex, face, vertex, degree, skeleton, subdivision and substructure, and prove some of their properties. MML identifier: SIMPLEX0, version: 7.11.01 4.117.1046...
متن کاملThe Genus of an Abstract Intersection Sequence
An intersection sequence, denoted IS, is a combinatorial object associated with a normal immersion/: S] -* M where S1 is an oriented circle and Af is a closed, connected, oriented 2-manifold. The genus of IS, denoted y(IS), is denned to be the smallest number which is the genus of a manifold M admitting a realization g: Sl -» M of IS. A method is given for computing y(IS) from IS. Throughout Sx...
متن کاملMaximal Sections of Sheaves of Data over an Abstract Simplicial Complex
We employ techniques from topological data analysis to model sensor networks. Our approach to sensor integration uses the topological method of sheaves over cell complexes. The internal consistency of data from individual sensors is determined by a set of consistency functions assigned to elements of the complex. Using these functions we determine, for any collection of data, the unique set of ...
متن کاملRandom Abstract Simplicial Complexes Reduction
Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network nodes without modifying neither the connectivity nor the coverage of the network. In this paper, we present a reduction algorithm that lower the number of points...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1940
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1940-07253-2