论文标题
截断的均质对称函数
Truncated Homogeneous Symmetric Functions
论文作者
论文摘要
扩展基本和完整的同质对称函数，我们介绍$（\ ref {thsf}）$ in $（\ ref {thsf}）$ in $（\ ref {thsf}）$ in $（\ ref {thsf}）$ in任何整数分区$λ$，并通过$h_λ^$ sym umm umm（ \ [m（h^{\ dd}，p）= m'（p，m）z^{ - 1} d^{\ dd}，\]，其中$ d^{\ dd} $和$ z $是非依次的二分法矩阵。因此，$ \ {h_λ^{\ dd} \} $形成对称函数的环$λ$的基础。此外，我们还表明生成函数$ h^{\ dd}（t）= \ ssum_ {n \ ge 0} h_n^{\ dd}（x）t^n $满足\ [ω（h^{h^{\ dd}（\ dd}（t）（t）（t）（t）） $ω$是$λ$的互动，将每个基本对称函数发送给完整的均质对称函数$H_λ$。
Extending the elementary and complete homogeneous symmetric functions, we introduce the truncated homogeneous symmetric function $h_λ^{\dd}$ in $(\ref{THSF})$ for any integer partition $λ$, and show that the transition matrix from $h_λ^{\dd}$ to the power sum symmetric functions $p_λ$ is given by \[M(h^{\dd},p)=M'(p,m)z^{-1}D^{\dd},\] where $D^{\dd}$ and $z$ are nonsingular diagonal matrices. Consequently, $\{h_λ^{\dd}\}$ forms a basis of the ring $Λ$ of symmetric functions. In addition, we show that the generating function $H^{\dd}(t)=\ssum_{n\ge 0}h_n^{\dd}(x)t^n$ satisfies \[ω(H^{\dd}(t))=\left(H^{\dd}(-t)\right)^{-1},\] where $ω$ is the involution of $Λ$ sending each elementary symmetric function $e_λ$ to the complete homogeneous symmetric function $h_λ$.
