2017/11/10 by D'Adderio, Michele, Iraci, Alessandro
#05E05 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.03923
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match ⟨ Δhm en+1, sk+1,1n-k ⟩, 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 ⟨Δ_em+n-k-1'em+n, hm hn ⟩ 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 Δ_hℓΔ_en-k-1'en, 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.