Tri-partitions and bases of an ordered complex

H. Edelsbrunner, K. Ölsböck, Discrete and Computational Geometry (2020).


Journal Article | Epub ahead of print | English

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Abstract
Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups.
Publishing Year
Date Published
2020-03-20
Journal Title
Discrete and Computational Geometry
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eISSN
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Cite this

Edelsbrunner H, Ölsböck K. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. 2020. doi:10.1007/s00454-020-00188-x
Edelsbrunner, H., & Ölsböck, K. (2020). Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry. https://doi.org/10.1007/s00454-020-00188-x
Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, 2020. https://doi.org/10.1007/s00454-020-00188-x.
H. Edelsbrunner and K. Ölsböck, “Tri-partitions and bases of an ordered complex,” Discrete and Computational Geometry, 2020.
Edelsbrunner H, Ölsböck K. 2020. Tri-partitions and bases of an ordered complex. Discrete and Computational Geometry.
Edelsbrunner, Herbert, and Katharina Ölsböck. “Tri-Partitions and Bases of an Ordered Complex.” Discrete and Computational Geometry, Springer Nature, 2020, doi:10.1007/s00454-020-00188-x.
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