TY - JOUR
AB - 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.
AU - Edelsbrunner, Herbert
AU - Ölsböck, Katharina
ID - 7666
JF - Discrete and Computational Geometry
SN - 01795376
TI - Tri-partitions and bases of an ordered complex
VL - 64
ER -