In a recent preprint, Carlsson and Oblomkov (Affine Schubert calculus and double coinvariants. arXiv preprint 1801.09033, 2018) obtain a long sought-after monomial basis for the ring \(\mathrm{D}\!\mathrm{R}_n\) of diagonal coinvariants. Their basis is closely related to the “schedules” formula for the Hilbert series of \(\mathrm{D}\!\mathrm{R}_n\) which was conjectured by the first author and Loehr (Discete Math 298(1–3):189–204, 2005) and first proved by Carlsson and Mellit (A proof of the shuffle conjecture. J Amer Math Soc 31(3):661–697, 2018), as a consequence of their proof of the famous Shuffle Conjecture. In this article, we obtain a schedules formula for the combinatorial side of the Delta Conjecture, a conjecture introduced by the Haglund et al. (Trans Am Math Soc 370(6):4029–4057, 2018), which contains the Shuffle Theorem as a special case. Motivated by the Carlsson–Oblomkov basis for \(\mathrm{D}\!\mathrm{R}_n\) and our Delta schedules formula, we introduce a (conjectural) basis for the super-diagonal coinvariant ring \(\mathrm{S}\!\mathrm{D}\!\mathrm{R}_n\), an \(S_n\)-module generalizing \(\mathrm{D}\!\mathrm{R}_n\) introduced recently by Zabrocki (a module for the Delta conjecture. arXiv preprint 1902.08966, 2019), which conjecturally corresponds to the Delta Conjecture.

在最近的预印本中，Carlsson和Oblomkov（Affine Schubert演算和双协变量。arXiv预印本1801.09033，2018年）为环\（\ mathrm {D} \！\ mathrm {R} _n \）获得了广受欢迎的单项式对角协变量。它们的基础与\（\ mathrm {D} \！\ mathrm {R} _n \）的Hilbert系列的“计划”公式密切相关。它由第一作者和Loehr猜想（Discete Math 298（1-3）：189-204，2005年），并首先由Carlsson和Mellit证明（随机猜想的证明。J Amer Math Soc 31（3）：661 –697，2018），因为他们证明了著名的洗牌猜想。在本文中，我们获得了Delta猜想（由Haglund等人提出的猜想）的组合方面的时间表公式。（Trans Am Math Soc 370（6）：4029-4057，2018年），其中包含作为特殊情况的随机定理。根据\（\ mathrm {D} \！\ mathrm {R} _n \）的Carlsson–Oblomkov基础和我们的Delta计划公式，我们为超对角协变环\（\ mathrm { S} \！\ mathrm {D} \！\ mathrm {R} _n \），一个\（S_n \）-模块概括Zabrocki（Delta猜想的模块。arXiv预印本1902.08966，2019 ）最近引入了\（\ mathrm {D} \！\ mathrm {R} _n \），它在推测上对应于Delta Conjecture。