论文标题
Nakayama代数的同源代数和321个避免排列
Homological algebra of Nakayama algebras and 321-avoiding permutations
论文作者
论文摘要
线性nakayama代数$ k $是自然对戴克路径的自然培养，而戴克路径则是通过Billey-Jockusch-Stanley Biovion进行的自然射击对321个避开321个范围的徒步。因此，对于每321个避免置换$π$，我们就可以自然地与线性中山代数$a_π$交往。我们使用Nakayama代数和线性颤抖给出了321个避免置换的固定点统计量的同源解释。我们此外表明，线性nakayama代数$a_π$的jacobson根部的自我扩展空间是同构为$ k^{\ mathfrak {s} {s}（π）} $，其中$ \ mathfrak {s}}（s}（π）$的$ k $ as the $ k $ s ins of the $ k is astry y IS y mim oun $ s_i =（i，i+1）$和$ k $是出现的不同$ s_i $的数量。
Linear Nakayama algebras over a field $K$ are in natural bijection to Dyck paths and Dyck paths are in natural bijection to 321-avoiding bijections via the Billey-Jockusch-Stanley bijection. Thus to every 321-avoiding permutation $π$ we can associate in a natural way a linear Nakayama algebra $A_π$. We give a homological interpretation of the fixed points statistic of 321-avoiding permutations using Nakayama algebras with a linear quiver. We furthermore show that the space of self-extension for the Jacobson radical of a linear Nakayama algebra $A_π$ is isomorphic to $K^{\mathfrak{s}(π)}$, where $\mathfrak{s}(π)$ is defined as the cardinality $k$ such that $π$ is the minimal product of transpositions of the form $s_i=(i,i+1)$ and $k$ is the number of distinct $s_i$ that appear.
