2025/12/22 by Atli Fannar Franklín, Franklín, Atli Fannar
Biochemistry, Genetics and Molecular Biology · Mathematics · #05A05 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Genome Rearrangement Algorithms #Markov Chains and Monte Carlo Methods
paper · doi:10.48550/arxiv.2512.19462
openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
The Stanley-Wilf limit of the pattern 1324 is known to lie between 10.271 and 13.5. We obtain lower bounds on this limit by encoding permutations as walks in directed graphs: building a permutation by successive insertion of maxima corresponds to traversing edges, and the growth rate of walks equals the spectral radius of the adjacency matrix. For 1324, this graph is too large for direct computation, so we pass to a quotient graph with weighted edges. Conditional on a natural conjecture, this yields a lower bound of 10.418.