论文标题
装饰的堤防路径，多支路和三角洲的猜想
Decorated Dyck paths, polyominoes, and the Delta conjecture
论文作者
论文摘要
我们讨论了装饰的戴克路径和饰有平行四边形多支着的组合，并扩展到装饰的情况下，[Haglund 2004]和[Aval等人。 2014]。这尤其解决了$ \ langle \ cdot，e_ {n-d} h_d \ rangle $和$ \ langle \ cdot，h_ {n-d} h_d \ rangle $ of Haglund，Remmel和Wilson（2018）。在此过程中，我们介绍了一些新的统计数据，制定了一些新的猜想，证明了对称功能的一些新身份，并回答了文献中的一些开放问题（例如，摘自[Haglund etal。2018]，[Zabrocki 2016]，[Zabrocki 2016]，[Aval等人2015]）。主要的技术工具是麦克唐纳多项式理论中的一种新身份，它扩展了[Haglund 2004]中Haglund定理的定理。这是Arxiv的编辑合并：1712.08787和Arxiv：1709.08736
We discuss the combinatorics of decorated Dyck paths and decorated parallelogram polyominoes, extending to the decorated case the main results of both [Haglund 2004] and [Aval et al. 2014]. This settles in particular the cases $\langle\cdot,e_{n-d}h_d\rangle$ and $\langle\cdot,h_{n-d}h_d\rangle$ of the Delta conjecture of Haglund, Remmel and Wilson (2018). Along the way, we introduce some new statistics, formulate some new conjectures, prove some new identities of symmetric functions, and answer a few open problems in the literature (e.g. from [Haglund et al. 2018], [Zabrocki 2016], [Aval et al. 2015]). The main technical tool is a new identity in the theory of Macdonald polynomials that extends a theorem of Haglund in [Haglund 2004]. This is an edited merge of arXiv:1712.08787 and arXiv:1709.08736
