The square form of the Delta conjecture

From papers

Let n1n\geq1, let PSQE(n)\mathsf{PSQ^E}(n) be the relevant set of square paths, and let δ(P)\delta(P) be the dinv reading word of PP. Write Des(δ(P))\mathsf{Des}(\delta(P)) for its descent set and QDes(δ(P)),nQ_{\mathsf{Des}(\delta(P)),n} for the associated quasisymmetric function. The square Delta conjecture.

Δen1en=PPSQE(n)qdinv(P)tarea(P)QDes(δ(P)),n.\Delta_{e_{n-1}}e_n=\sum_{P\in\mathsf{PSQ^E}(n)}q^{\mathsf{dinv}(P)}t^{\mathsf{area}(P)}Q_{\mathsf{Des}(\delta(P)),n}.

This is introduced as a square reformulation of the Δen1en\Delta_{e_{n-1}}e_n case of the Delta conjecture. The excerpt does not state a proof of this identity, so it remains open as a conjectural formulation.

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Sources & referencesView supporting material

Primary source

Michele D'Adderio, Alessandro Iraci and Anna Vanden Wyngaerd, “Decorated Dyck paths, polyominoes, and the Delta conjecture”, arXiv:2011.09568 (2020).

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