• Corpus ID: 207870987

On Approximation of $2$D Persistence Modules by Interval-decomposables

@article{Asashiba2019OnAO,
  title={On Approximation of \$2\$D Persistence Modules by Interval-decomposables},
  author={Hideto Asashiba and Emerson G. Escolar and Ken Nakashima and Michio Yoshiwaki},
  journal={arXiv: Representation Theory},
  year={2019}
}
In this work, we propose a new invariant for $2$D persistence modules called the compressed multiplicity and show that it generalizes the notions of the dimension vector and the rank invariant. In addition, we propose an "interval-decomposable approximation" $\delta^{\ast}(M)$ of a $2$D persistence module $M$. In the case that $M$ is interval-decomposable, we show that $\delta^{\ast}(M) = M$. Furthermore, even for representations $M$ not necessarily interval-decomposable, $\delta^{\ast}(M… 

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