14 problems

Subdivided-sweep conjecture. There is a faster way to compute all cokernels of $M_{\leq g}$ for $g \in G$ in one sweep, with runtime in $\mathcal{O}(dn^3)$, rather than calling the…

The generalized persistence diagram and the spread-Euler characteristic are invariants associated with finitely presented multiparameter persistence representations; on a fixed spr…

Bjerkevik's conjecture. On persistence modules of bounded pointwise dimension, the pruning distance is stable and Lipschitz equivalent to the interleaving distance. More precisely,…

Let $M$ be a multiparameter persistence module and let an $varepsilon$-pruning be its decomposable approximation obtained by discarding features below scale $varepsilon$. Bjerkevik…

Finiteness conjecture. Under generic conditions on the input pair $(\bo\p,\bo\s)$, this special subset of $[0,1]$ is finite.

Finiteness conjecture. The set

Let $c\geq 1$ be an odd integer, and let $(P,Q)$ be a compatible-inclusion problem, with its $c$-weakening defined by retaining directed edges represented by paths of length at mos…

Let $M$ and $N$ be upset decomposable persistence modules, where an upset decomposable module is a direct sum of upset modules. The upset matching conjecture. There is a constant…

Let a persistence module be given in the computational setting of the paper, and let its pruning be the invariant defined there. The polynomial-time pruning conjecture. Computing p…

Let $M$ and $N$ be persistence modules that are $\epsilon$-interleaved, with $\epsilon\geq 0$. Let … Here $B(M)$ is the relevant neighborhood of $M$ defined in the paper, and an…

Let $M$ and $N$ be pfd persistence modules, and let $d_P$ denote the pruning distance and $d_I$ the interleaving distance. Write $r=\operatorname{supdim}M<\infty$. The pruning-dist…

Cubic Betti-number bound. We have

Let $n\geq 3$ be fixed, and consider $n$-parameter persistence modules equipped with the relevant distance and interleaving distance. The paper notes that the 1-Lipschitz stability…

Let $n\geq 1$ be fixed, and let $d^p_{\mathcal{M}}$ and $d^p_{\mathcal I}$ denote the corresponding distances on finitely presented $n$-parameter persistence modules, with…