Abstract We establish a bijection between $d$-simple-minded systems ($d$-SMSs) of $(-d)$-Calabi–Yau cluster category $\mathcal C_{-d}(H)$ and silting objects ${\mathcal {D}}^{\mathrm {b}}(H)$ contained in {D}}^{\le 0}\cap {\mathcal {D}}^{\ge 1-d}$ for hereditary algebra $H$ Dynkin type $d\ge 1$. show that the number $d$-SMSs is positive Fuss–Catalan $C_{d}^{+}(W)$ corresponding Weyl group $W$, ...

Abstract We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without object. Second, study two classes $\tau$ -tilting-finite algebras and give numbers their two-term Finally, explore when -tilting-finiteness implies representation-finiteness obtain several in which a algebra is representation-finite.

The paper analyzes spatial features and long-term dynamics of silting the Krasnodar Reservoir, key object entire reclamation system region with a 3.35 billion m3 annual limit water intake for irrigation; analysis is based on bathymetric survey data. Accurate up-to-date estimates siltation volumes changes in hydrometric characteristics reservoir are necessary to develop correct strategy consumpt...

We describe the derived Picard groups and two-term silting complexes for quasi-hereditary algebras with two simple modules. also by quivers relations all equivalent to a algebra