论文标题
理性$ Q，T $ -CATALAN多项式的猜想公式
A conjectured formula for the rational $q,t$-Catalan polynomial
论文作者
论文摘要
我们猜想有理$ q，t $ -catalan pytermial $ \ mathcal {c} _ {r/s} $对称为$ q $和$ t $的公式。该猜想认为$ \ Mathcal {C} _ {r/s} $可以用最大戴克路径索引的对称单体字符串编写。我们证明，对于任何有限的$ d^*$，给出了我们对无限函数集$ \ {\ Mathcal {c} _ {r/s}^d：r \ equiv 1 \ mod S，\，\，\，\，\，\，d \ leq d^*\ \ e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e earitive的组合证明。
We conjecture a formula for the rational $q,t$-Catalan polynomial $\mathcal{C}_{r/s}$ that is symmetric in $q$ and $t$ by definition. The conjecture posits that $\mathcal{C}_{r/s}$ can be written in terms of symmetric monomial strings indexed by maximal Dyck paths. We show that for any finite $d^*$, giving a combinatorial proof of our conjecture on the infinite set of functions $\{ \mathcal{C}_{r/s}^d: r\equiv 1 \mod s, \,\,\, d \leq d^*\}$ is equivalent to a finite counting problem.
