Composition-partition invariance conjecture for Dyck graphs
Let G=([n],E)G=([n],E)G=([n],E) be a Dyck graph. For a composition α⊨n\alpha\vDash nα⊨n, let λ(α)\lambda(\alpha)λ(α) be the partition obtained by rearranging its parts, and let NG,α\mathcal{N}_{G,\alpha}NG,α be t…