Institute for Advanced Study

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20242026

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math.RT2026

Interval Multiplicities of Persistence Modules

Hideto Asashiba, Enhao Liu

For any persistence module $M$ over a finite poset $P$ , and any interval $I$ of $P$ , we give a formula for the multiplicity $d_{M} (V_{I})$ of the interval module $V_I…

math.RT2026

Interval Replacements of Persistence Modules

Hideto Asashiba, Etienne Gauthier, Enhao Liu

We define two notions. The first one is a $r ank co m p r ess i o n sy s t e m$ $I^¾$ for a finite poset $P$ that assigns each interval subposet $I$ to an order-preserving map $Î¾_I…