论文标题
Robinson-Schensted单位间隔顺序
Robinson-Schensted correspondence for unit interval orders
论文作者
论文摘要
Stanley-Stembridge猜想将对称功能与每个自然单位间隔顺序$ \ MATHCAL P $相关联。在本文中，我们为每个$ \ mathcal p $在对称组上定义了关系àlaknuth，并认为相关的$ \ Mathcal p $ -knuth等价类是Schur阳性的，是Gasharov，Brosnan-Chow和Guay-Paquet的Gasharov定理。所得的等效图适合ASSAF研究的D图的框架。此外，我们猜想Schur扩展是由等价类中发生的$ \ Mathcal P $ -TableAux的列阅读给出的。我们通过引入$ \ Mathcal p $ -Analog of Robinson-Schensted插入来证明这些猜想的$ \ Mathcal P $避免了两个特定的子词，从而回答了长期存在的Chow问题。
The Stanley-Stembridge conjecture associates a symmetric function to each natural unit interval order $\mathcal P$. In this paper, we define relations à la Knuth on the symmetric group for each $\mathcal P$ and conjecture that the associated $\mathcal P$-Knuth equivalence classes are Schur-positive, refining theorems of Gasharov, Brosnan-Chow, and Guay-Paquet. The resulting equivalence graphs fit into the framework of D graphs studied by Assaf. Furthermore, we conjecture that the Schur expansion is given by column-readings of $\mathcal P$-tableaux that occur in the equivalence class. We prove these conjectures for $\mathcal P$ avoiding two specific suborders by introducing $\mathcal P$-analog of Robinson-Schensted insertion, giving an answer to a long standing question of Chow.
