The Ascbot shape-Wilf equivalence conjecture for 231⊕σ and 312⊕σ
The Ascbot shape-Wilf equivalence conjecture for 231⊕σ and 312⊕σ
Let be a nonempty permutation, let denote their direct sum, and let be a traversable Ferrers board. For a traversal of , define the -ascent bottom statistic from the ascent bottoms in its separated traversal. Two patterns are -shape-Wilf equivalent if, for every traversable board , there is a bijection between their -avoiders preserving . The Ascbot shape-Wilf conjecture. For any nonempty permutation , the patterns and are -shape-Wilf equivalent. This claim is obtained in the source from complementing the analogous descent-top assertion; its status is not resolved in the supplied text.
Sources & referencesView supporting material
Primary source
Alexander Burstein, “Distribution of sets of descent tops and descent bottoms on restricted permutations”, arXiv:2306.08065 (2025).
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