A restricted model for the bounded derived category of gentle algebras

We present a restricted model for the bounded derived category of gentle algebras that encodes the indecomposable objects and positive extensions between them. The model is then used to count the number of $d$-term silting objects for linearly oriented $A_n$, recovering the result that they are counted by the Pfaff-Fuss-Catalan numbers.
Comment: 13 pages