AI 中文总结
该研究针对两类嵌套避免模式排列的生成函数，建立q-差分方程并求解，证明其非D-有限，还给出了两类生成函数系数的渐近行为
AI 中文摘要
我们研究嵌套排列类Av(4123,4231,4312)⊂Av(4123,4312)，将对应生成函数D⁽²⁾(z)、D⁽³⁾(z)与q-差分方程关联，求解后证明这些生成函数非D-有限，且[zⁿ]D⁽³⁾(z)~0.0189672325071988…(4.46840899160393…)ⁿ，[zⁿ]D⁽²⁾(z)~0.0849833632890843…(3+2√2)ⁿn⁻³/₂
英文摘要
We study the nested permutation classes $Av(4123,4231,4312)\subset Av(4123,4312)$. We relate the corresponding generating functions $D^{(2)}(z)$, $D^{(3)}(z)$ to $q$-difference equations. Solving these equations allows to show that the generation functions are not D-finite, and that $[z^n]D^{(3)}(z)\sim 0.0189672325071988\ldots\, (4.46840899160393\ldots)^n$, $[z^n]D^{(2)}(z)\sim0.0849833632890843\ldots\, (3+2\sqrt2)^n n^{-3/2}$.
