Titlebook: Boolean Representations of Simplicial Complexes and Matroids; John Rhodes,Pedro V. Silva Book 2015 Springer International Publishing Switz

骂人有污点

https://doi.org/10.1007/978-3-319-02057-0In this chapter we begin the main subject of this monograph, boolean representations of simplicial complexes. In view of the correspondences established in Sects. 3.4 and 3.5, lattices play a major role.

动作谜

Nonlinear Systems and ComplexityWe devote this chapter to the particular case of paving simplicial complexes, with special emphasis on the case of dimension 2. We shall develop tools such as the graph of flats, which will lead us in Chap. 7 to results involving the geometric realization of the complex.

图画文字

Nonlinear Systems and ComplexityIn this section, we relate shellability of a simplicial complex . with certain properties of its graph of flats. We then use shellability to determine the homotopy type of the geometric realization . (see Sect. A.5 in the Appendix) and compute its Betti numbers.

elastic

缺乏

Localized Excitations in SolidsAs a general objective we would like to raise the results in this monograph from dimension 2 to dimension 3 and further.

小虫

Boolean and Superboolean Matrices,We introduce in this chapter the superboolean semiring . and the core of the theory of (boolean) matrices over ., with special emphasis on the concepts of independence of vectors and rank. These matrices are used to represent various kinds of algebraic and combinatorial objects, namely posets and simplicial complexes, especially matroids.

炸坏

整理

monochromatic

Corral

Paving Simplicial Complexes,We devote this chapter to the particular case of paving simplicial complexes, with special emphasis on the case of dimension 2. We shall develop tools such as the graph of flats, which will lead us in Chap. 7 to results involving the geometric realization of the complex.