@article{Nategh2025, 
author = {Mehdi Nategh and Zhenbo Qin and Shuguang Wang},
title = {N        d  -Indexed persistence modules, higher dimensional partitions and rank invariants},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {11},
pages = {25589-25605},
keywords = {multiparameter persistence, Nd-indexed persistence modules, higher dimensional partitions, rank invariants, barcodes, Young diagrams},
url = {https://www.sciopen.com/article/10.3934/math.20251133},
doi = {10.3934/math.20251133},
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.}
}