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- W2767664657 abstract "We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $langle Delta_{h_m} e_{n+1}, s_{k+1,1^{n-k}} rangle$, extending in this way the work in (Aval et al. 2014). Also, we provide a bijective connection between decorated parallelogram polyominoes and decorated labelled Dyck paths, which allows us to prove the combinatorial interpretation of the coefficient $langleDelta_{e_{m+n-k-1}}'e_{m+n}, h_m h_n rangle$ predicted by the Delta conjecture in (Haglund et al. 2015). Finally, we define a statistic pmaj on partially labelled Dyck paths, which provides another conjectural combinatorial interpretation of $Delta_{h_{ell}}Delta_{e_{n-k-1}}'e_n$, cf. (Haglund et al. 2015). This is an extended abstract of (D'Adderio, Iraci 2017): this forthcoming publication will have proofs and additional details and results." @default.
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- W2767664657 date "2017-11-10" @default.
- W2767664657 modified "2023-10-03" @default.
- W2767664657 title "Parallelogram polyominoes, partially labelled Dyck paths, and the Delta conjecture" @default.
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