2023/12/04 by Alperen Y. Özdemir, Özdemir, Alperen
Biochemistry, Genetics and Molecular Biology · Computer Science · #03C13 #60C05 #60G07 #Bayesian Methods and Mixture Models #FOS: Mathematics #Genome Rearrangement Algorithms #Probability (math.PR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2312.01749
openalex publication_date 2023/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We say that a convergence law holds for a sequence of random combinatorial objects if, for any first-order sentence φ, the proportion of objects satisfying φ converges to a limiting value as the size of the objects tends to infinity. In this paper, we show that the convergence law holds for random 321-avoiding permutations, settling an open problem posed in Albert, Bouvel, Féray, and Noy (2024). Our proof relies on an infinite-dimensional version of the Perron-Frobenius theorem.