2024/05/22 by Alexander Burstein, Tian Han, Burstein, Alexander +5 · 1 citation
Business, Management and Accounting · #05A05 (Primary) 05A15 #05A19 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Optics and Image Analysis
paper · pdf · doi:10.48550/arxiv.2405.14041
openalex publication_date 2024/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a conjecture of Gao and Kitaev on Wilf-equivalence of sets of patterns 12345,12354 and 45123,45213 that extends the list of 10 related conjectures proved in the literature in a series of papers. To achieve our goals, we prove generalized versions of shape-Wilf-equivalence results of Backelin, West, and Xin and use a particular result on shape-Wilf-equivalence of monotone patterns. We also derive general results on shape-Wilf-equivalence of certain classes of partially ordered patterns and use their specialization (also appearing in a paper by Bloom and Elizalde) as an essential piece in proving the conjecture. Our results allow us to show (shape-)Wilf-equivalence of large classes of sets of patterns, including 11 out of 12 classes found by Bean et al. in relation to the conjecture.