Year: 2026
Type: preprint
Abstract: 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 $[z^n]D^{(3)}(z)\sim 0.0189672325071988\ldots\, (4.46840899160393\ldots)^n$, $[z^n]D^{(2)}(z)\sim0.0849833632890843\ldots\, (3+2\sqrt2)^n n^{-3/2}$.
Source: arXiv (Cornell University)
Author: Zinn-Justin, Paul
Institution: The University of Melbourne
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202204367
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