Geodesic
On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns
Alexander Burstein ; Tian Han ; Sergey Kitaev ; Philip B. Zhang1
1Tianjin Normal University
The electronic journal of combinatorics, Tome 32 (2025) no. 1
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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.
DOI : 10.37236/13037
Classification : 05A05, 05A15, 05A19
Mots-clés : permutation pattern, Wilf-equivalence, shape-Wilf-equivalence, partially ordered pattern

Alexander Burstein    ; Tian Han    ; Sergey Kitaev    ; Philip B. Zhang  1

1 Tianjin Normal University 
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     title = {On {(shape-)Wilf-equivalence} of certain sets of (partially ordered) patterns},
     journal = {The electronic journal of combinatorics},
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Alexander Burstein; Tian Han; Sergey Kitaev; Philip B. Zhang. On (shape-)Wilf-equivalence of certain sets of (partially ordered) patterns. The electronic journal of combinatorics, Tome 32 (2025) no. 1. doi: 10.37236/13037

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