带有正则单模的Nakayama代数的计数
Counting Nakayama Algebras with Regular Simple Modules

有限生成投射模范畴的正合结构的分类与2正则单模有关。基于Nakayama代数上的正则单模的代数性质与Dyck路的组合结构的对应，计算了带有k个1正则单模(或k个2正则单模)的(n + 1)-LNakayama代数和拟遗传n-CNakayama代数的个数。
The classification of exact structures in the category of finitely generated projective modules for finite dimensional algebras were reduced to the classification of 2-regular simple modules. By the result of relations between regular simple modules over Nakayama algebras and certain combinatorial structures of Dyck paths, the number of (n + 1)-LNakayama algebras and quasi-hereditary n-CNakayama algebras that have exactly k 1-regular simple modules (respectively k 2-regular simple modules) was calculated.