论文标题
无三角形水平条纹LLT多项式的组合Schur扩展
A combinatorial Schur expansion of triangle-free horizontal-strip LLT polynomials
论文作者
论文摘要
近年来，Alexandersson和其他人在某些特殊情况下，证明了水平折线LLT多项式$G_λ（X; Q）$的Schur功能扩展的组合公式。我们将加权图$π$与$λ$相关联，我们使用它来表达LLT多项式之间的线性关系。我们应用此关系以证明$g_λ（x; q）$的显式组合Schur阳性扩展，只要$π$不含三角形。我们还证明，LLT多项式中$ Q $的最大功率是我们图形的总边缘重量。
In recent years, Alexandersson and others proved combinatorial formulas for the Schur function expansion of the horizontal-strip LLT polynomial $G_λ(x;q)$ in some special cases. We associate a weighted graph $Π$ to $λ$ and we use it to express a linear relation among LLT polynomials. We apply this relation to prove an explicit combinatorial Schur-positive expansion of $G_λ(x;q)$ whenever $Π$ is triangle-free. We also prove that the largest power of $q$ in the LLT polynomial is the total edge weight of our graph.
