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arXiv · 2510.23811

N^d-indexed persistence modules, higher dimensional partitions and rank invariants

Mehdi Nategh·Zhenbo Qin·Shuguang Wang
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Abstract

We study decomposable N^d-indexed persistence modules via higher dimensional partitions. Their barcodes are defined in terms of the extended interior of the corresponding Young diagrams. For two decomposable N^d-indexed persistence modules, we present a necessary and sufficient condition, in terms of the partitions, for their rank invariants to be the same. This generalizes the well-known fact that for an N-indexed persistence module, its barcode and its rank invariant determine each other, i.e., the rank invariant is a complete invariant.

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Mehdi Nategh, Zhenbo Qin, Shuguang Wang. 2025-10-27. N^d-indexed persistence modules, higher dimensional partitions and rank invariants. https://arxiv.org/abs/2510.23811

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