Year: 2024
Type: article
Abstract: We prove that the class of 231-avoiding permutations satisfies a logical limit law, i.e. that for any first-order sentence $\Psi$, in the language of two total orders, the probability $p_{n,\Psi}$ that a uniform random 231-avoiding permutation of size $n$ satisfies $\Psi$ admits a limit as $n$ is large. Moreover, we establish two further results about the behavior and value of $p_{n,\Psi}$: (i) it is either bounded away from $0$, or decays exponentially fast; (ii) the set of possible limits is dense in $[0,1]$. Our tools come mainly from analytic combinatorics and singularity analysis.
DOI: 10.46298/dmtcs.11751
Institutions: University of Otago, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire Lorrain de Recherche en Informatique et ses Applications, Université de Lorraine, Institut Élie Cartan de Lorraine, Universitat Politècnica de Catalunya
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4393437542