N^d-indexed persistence modules, higher dimensional partitions and rank invariants
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914117662539776 |
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| author | Nategh, Mehdi Qin, Zhenbo Wang, Shuguang |
| author_facet | Nategh, Mehdi Qin, Zhenbo Wang, Shuguang |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | N^d-indexed persistence modules, higher dimensional partitions and rank invariants Nategh, Mehdi Qin, Zhenbo Wang, Shuguang Algebraic Topology Algebraic Geometry Combinatorics 55N31, 14C05, 05A17 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. |
| title | N^d-indexed persistence modules, higher dimensional partitions and rank invariants |
| topic | Algebraic Topology Algebraic Geometry Combinatorics 55N31, 14C05, 05A17 |
| url | https://arxiv.org/abs/2510.23811 |