Tri-partitions and Bases of an Ordered Complex

@article{Edelsbrunner2020TripartitionsAB,
  title={Tri-partitions and Bases of an Ordered Complex},
  author={H. Edelsbrunner and K. {\"O}lsb{\"o}ck},
  journal={Discrete & Computational Geometry},
  year={2020},
  pages={1-17}
}
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… Expand
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