@article{Wen2024, 
author = {Haicun Wen and Mian-Tao Liu and Yu-Zhe Liu},
title = {The counting formula for indecomposable modules over string algebra},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {9},
pages = {24977-24988},
keywords = {representation-finite, representations of quivers, indecomposable modules},
url = {https://www.sciopen.com/article/10.3934/math.20241217},
doi = {10.3934/math.20241217},
abstract = {Let  A=kQ/I be a string algebra. We show that, if for any vertex  v of its bound quiver  (Q,I), there exists at most one arrow (resp. at most two arrows) ending with  v and there exist at most two arrows (resp. at most one arrow) starting with  v, then the number of indecomposable modules over  A is  dimk⁡A+Σ, where  Σ is induced by  radP(v) (resp.  E(v)/socE(v)) with decomposable socle (resp. top), where  P(v) (resp.  E(v)) is the indecomposable projective (resp. injective) module corresponded by the vertex  v.}
}