1. On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns
- Author
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Burstein, Alexander, Han, Tian, Kitaev, Sergey, and Zhang, Philip
- Subjects
Mathematics - Combinatorics ,05A05 (Primary) 05A15, 05A19 (Secondary) - Abstract
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., Comment: 9 pages, 3 figures
- Published
- 2024