# Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions

@article{Botnan2021SignedBF, title={Signed Barcodes for Multi-Parameter Persistence via Rank Decompositions and Rank-Exact Resolutions}, author={Magnus Bakke Botnan and Steffen Oppermann and Steve Oudot}, journal={ArXiv}, year={2021}, volume={abs/2107.06800} }

In this paper we introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode encodes the rank invariant as a Z-linear combination of rank invariants of indicator modules supported on segments in the poset. It can also be enriched to encode the generalized rank invariant as a Z-linear… Expand

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