# The Shift-Dimension of Multipersistence Modules

@inproceedings{Chacholski2021TheSO, title={The Shift-Dimension of Multipersistence Modules}, author={Wojciech Chach'olski and Ren{\'e} Corbet and Anna-Laura Sattelberger}, year={2021} }

. We present the shift-dimension of multipersistence modules and investigate its algebraic properties. This gives rise to a new invariant of multigraded modules over the multivariate polynomial ring arising from the hierarchical stabilization of the zeroth total multigraded Betti number. We give a fast algorithm for the computation of the shift-dimension of interval modules in the bivariate case. We construct multipersistence contours that are parameterized by multivariate functions and hence…

## 2 Citations

### Multiparameter persistence modules in the large scale

- Mathematics
- 2022

. A persistence module with m discrete parameters is a diagram of vector spaces indexed by the poset N m . If we are only interested in the large scale behavior of such a diagram, then we can…

### On the bottleneck stability of rank decompositions of multi-parameter persistence modules

- Mathematics, Computer ScienceArXiv
- 2022

The signed barcode induced by the Betti numbers of the module relative to the so-called rank exact structure is proved to be bottleneck stable under signed matchings and a bottleneck stability result for hook-decomposable modules is proved.

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