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

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Shellability and Homotopy Type,In 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.

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Operations on Simplicial Complexes,We consider in this chapter various natural operations on simplicial complexes and study how they relate to boolean representability. The particular case of restrictions will lead us to introduce prevarieties of simplicial complexes and finite basis problems.

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Open Questions,As a general objective we would like to raise the results in this monograph from dimension 2 to dimension 3 and further.

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Introduction,: it is well known that not all matroids admit a field representation [39]. Attempts have been made to replace fields by more general structures such as . [49] or . [18], but they still failed to cover all matroids.

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Book 2015es featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended contex

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Book 2015t opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes..

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Boolean Representations of Simplicial Complexes and Matroids