论文标题
$ {\ textsf {qSym}} $的分类使用surestracter理论和$ {\ textsf {nsym}}} _ {\ mathbb {c}（q，q，t）} $的新基础
Categorifications of ${\textsf {QSym}}$ using supercharacter theories and a new basis for ${\textsf {NSym}}_{\mathbb{C}(q,t)}$
论文作者
论文摘要
让我们修复一个正整数$ν> 1 $。对于每个积极整数$ n> 1 $，我们考虑了$ g_n $的普通辐射理论$ \ mathcal {s} _n $，其中$ g_n $是$ n-1 $ copies of Cyclic of Cyclic of Cyclic of Comclic of Comclic of Complot of订单$ν$的直接产品。然后，我们endow $ \ bigoplus_ {n \ ge 0} \ textsf {scf}（\ Mathcal {s} _n）$，superchacter函数空间的直接产物，Hopf代数结构与Hopf Algebra and hopf Algebra $ hopf algebra $ \ textsf ism fortsym is hopf代数结构。此外，我们计算了由超类标识符函数组成的基础获得的HOPF代数的结构常数。使用我们的分类，我们研究了Hopf代数$ \ textsf {nsym} _ {\ Mathbb {c}（q，q，t）} $在合理函数$ \ mathbb {c}（q，q，q，q，q，q，q，q，q，q，q，q，q，q，q，q，q，q，q， $ \ textsf {nsym} _ {\ mathbb {c}（q，t）} $此基础。还可以通过$ Q $和$ t $的专业提取一些有趣的应用程序。
Let us fix a positive integer $ν>1$. For each positive integer $n>1$, we consider a normal supercharacter theory $\mathcal{S}_n$ of $G_n$, where $G_n$ is the direct-product of $n-1$ copies of the cyclic group of order $ν$. Then we endow $\bigoplus_{n \ge 0} \textsf{scf}(\mathcal{S}_n)$, the direct-product of supercharacter function spaces, with the Hopf algebra structure that is isomorphic to the Hopf algebra $\textsf{QSym}$ of quasisymmetric functions. Furthermore, we compute the structure constants of the Hopf algebra thus obtained for the basis consisting of superclass identifier functions. Using our categorifications, we study a new basis for the Hopf algebra $\textsf{NSym}_{\mathbb{C}(q,t)}$ of noncommutative symmetric functions over the rational function field $\mathbb{C}(q,t)$ in commuting variables $q$ and $t$, with an emphasis on the structure constants of $\textsf{NSym}_{\mathbb{C}(q,t)}$ for this basis. Some interesting applications are also obtained via the specializations of $q$ and $t$.
