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- W2963567580 abstract "In this paper we examine the descriptive potential of a combinatorial data structure known as Set in constructing the boundary maps of a simplicial complex. By refining the approach of cite{Dumas} in generating these maps, we provide algorithms that allow for relations among simplices to be easily accounted for. In this way we explicitly generate faces of a complex only once, even if a face is shared among multiple simplices. The result is a useful interface for constructing complexes with many relations and for extending our algorithms to $Delta$-complexes. Once we efficiently retrieve the representatives of living simplices i.e., of those that have not been related away, the construction of the boundary maps scales well with the number of relations and provides a simpler alternative to JPlex. We finish by noting that the generating data of a complex is equivalent in information to its incidence matrix and we provide efficient algorithms for converting from an incidence matrix to a Generating Set." @default.
- W2963567580 created "2019-07-30" @default.
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- W2963567580 date "2018-04-01" @default.
- W2963567580 modified "2023-09-23" @default.
- W2963567580 title "Generating Minimal Boundary Maps" @default.
- W2963567580 doi "https://doi.org/10.13189/ms.2018.060202" @default.
- W2963567580 hasPublicationYear "2018" @default.
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