Positive Fuss-Catalan numbers and Simple-minded systems in negative Calabi-Yau categories

Osamu Iyama, Haibo Jin

We establish a bijection between $d$-simple-minded systems ($d$-SMSs) of $(-d)$-Calabi-Yau cluster category ${\mathcal{C}}_{-d}(H)$ and silting objects of ${\mathcal{D}}^{\mathrm{b}}(H)$ containe…