The Ascbot shape-Wilf equivalence conjecture for 231⊕σ and 312⊕σ

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Let σ\sigma be a nonempty permutation, let ρ⊕σ\rho\oplus\sigma denote their direct sum, and let FF be a traversable Ferrers board. For a traversal τ\tau of FF, define the FF-ascent bottom statistic Ascbot⁡F(τ)\operatorname{Ascbot}_F(\tau) from the ascent bottoms in its separated traversal. Two patterns are Ascbot⁡\operatorname{Ascbot}-shape-Wilf equivalent if, for every traversable board FF, there is a bijection between their FF-avoiders preserving Ascbot⁡F\operatorname{Ascbot}_F. The Ascbot shape-Wilf conjecture. For any nonempty permutation σ\sigma, the patterns 231⊕σ231\oplus\sigma and 312⊕σ312\oplus\sigma are Ascbot⁡\operatorname{Ascbot}-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.

References

Primary source

Alexander Burstein, “Distribution of sets of descent tops and descent bottoms on restricted permutations”, arXiv:2306.08065 (2025).

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