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- W4321151551 abstract "The systematic study of inversion sequences avoiding triples of relations was initiated by Martinez and Savage. For a triple $(rho_1,rho_2,rho_3)in{<,>,leq,geq,=,neq,-}^3$, they introduced $I_n(rho_1,rho_2,rho_3)$ as the set of inversion sequences $e=e_1e_2cdots e_n$ of length $n$ such that there are no indices $1leq i<j<kleq n$ with $e_i rho_1 e_j$, $e_j rho_2 e_k$ and $e_i rho_3 e_k$. To solve a conjecture of Martinez and Savage, Lin constructed a bijection between $I_n(geq,neq,>)$ and $I_n(>,neq,geq)$ that preserves the distinct entries and further posed a symmetry conjecture of ascents on these two classes of restricted inversion sequences. Concerning Lin's symmetry conjecture, an algebraic proof using the kernel method was recently provided by Andrews and Chern, but a bijective proof still remains mysterious. The goal of this article is to establish bijectively both Lin's symmetry conjecture and the $gamma$-positivity of the ascent polynomial on $I_n(>,neq,>)$. The latter result implies that the distribution of ascents on $I_n(>,neq,>)$ is symmetric and unimodal." @default.
- W4321151551 created "2023-02-18" @default.
- W4321151551 creator A5053756620 @default.
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- W4321151551 date "2021-12-07" @default.
- W4321151551 modified "2023-09-24" @default.
- W4321151551 title "Combinatorics of the symmetries of ascents in restricted inversion sequences" @default.
- W4321151551 doi "https://doi.org/10.48550/arxiv.2112.04115" @default.
- W4321151551 hasPublicationYear "2021" @default.
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