论文标题
$（p，q，t）$ - 加泰罗尼亚持续分数，伽马扩展和图案回避
$(p,q,t)$-Catalan continued fractions, gamma expansions and pattern avoidances
论文作者
论文摘要
我们引入了一种$（p，q，t）$ - 加泰罗尼亚类型A的加泰罗尼亚数字，通过概括雅各布类型的持续分数公式，我们证明了相应的扩展可以由多项式计数置换置于$§_n（321）$的$§_n（321）$。 Moreover, we introduce a kind of $(p, q, t)$-Catalan numbers of Type B by generalizing the Jacobian type continued fraction formula, we proved that the Taylor coefficients and their $γ$-coefficients could be expressed by the polynomials counting permutations on $§_n(3124, 4123, 3142, 4132)$ by various descent statistics.我们的方法包括涉及从置换模式到标记的Motzkin路径和修改的FOATA-STREHL动作的列表变化的置换枚举技术。
We introduce a kind of $(p, q, t)$-Catalan numbers of Type A by generalizing the Jacobian type continued fraction formula, we proved that the corresponding expansions could be expressed by the polynomials counting permutations on $§_n(321)$ by various descent statistics. Moreover, we introduce a kind of $(p, q, t)$-Catalan numbers of Type B by generalizing the Jacobian type continued fraction formula, we proved that the Taylor coefficients and their $γ$-coefficients could be expressed by the polynomials counting permutations on $§_n(3124, 4123, 3142, 4132)$ by various descent statistics. Our methods include permutation enumeration techniques involving variations of bijections from permutation patterns to labeled Motzkin paths and modified Foata-Strehl action.
