论文标题
山谷三角洲猜想的一些后果
Some consequences of the valley Delta conjectures
论文作者
论文摘要
在（Haglund，Remmel，Wilson 2018）Haglund，Remmel和Wilson引入了他们的Delta猜想，这些猜想给出了两种不同的组合解释$δ'_ {e_ {e_ {n-k-1}} e_n $，以崛起或瓦利被装修的二重装饰性染色的dyck paths contimentity相应地相对地。虽然最近已证明了Rise版本（D'Adderio，Mellit 2021； Blasiak，Haiman，Morse，Pun，Seelinger Preprint 2021），但对山谷版本并不了解。在这项工作中，我们证明了山谷三角洲猜想的Schröder案例，其Square版本的Schröder案例（Iraci，Vanden Wyngaerd 2021）以及其扩展版本的加泰罗尼亚案例（Qiu，Wilson，Wilson 2020）。此外，假设（改进）扩展山谷三角洲猜想的组合侧的对称性，我们还推断出其正方形版本的加泰罗尼亚案例（Iraci，iraci，vanden wyngaerd 2021）。
In (Haglund, Remmel, Wilson 2018) Haglund, Remmel and Wilson introduced their Delta conjectures, which give two different combinatorial interpretations of the symmetric function $Δ'_{e_{n-k-1}} e_n$ in terms of rise-decorated or valley-decorated labelled Dyck paths respectively. While the rise version has been recently proved (D'Adderio, Mellit 2021; Blasiak, Haiman, Morse, Pun, Seelinger preprint 2021), not much is known about the valley version. In this work we prove the Schröder case of the valley Delta conjecture, the Schröder case of its square version (Iraci, Vanden Wyngaerd 2021), and the Catalan case of its extended version (Qiu, Wilson 2020). Furthermore, assuming the symmetry of (a refinement of) the combinatorial side of the extended valley Delta conjecture, we deduce also the Catalan case of its square version (Iraci, Vanden Wyngaerd 2021).
