论文标题
在带有两个边界变量的准对称函数上
On Quasisymmetric Functions with Two Bordering Variables
论文作者
论文摘要
我们将过去的结果扩展到正式功率系列$ k_ {n，λ} $，由$ n $和$λ\ subseteq [n] $进行参数，这在很大程度上类似于准对称函数。这个功能系列被认为具有任何两个功能的产品$ k_ {n，λ} k_ {m，ω} $的属性$ k_ {n，λ} $和$ k_ {m，ω} $可以作为家族的线性组合表达为家族的线性组合。在本文中，我们表明确实是这种情况，并且$ k_ {n，λ} $的跨度形成了代数。我们还提供了检查类似功能系列的技术和产品的公式$ k_ {n，λ} k_ {m，ω} $当$ n = 1 $时。
We extend past results on a family of formal power series $K_{n, Λ}$, parameterized by $n$ and $Λ\subseteq [n]$, that largely resemble quasisymmetric functions. This family of functions was conjectured to have the property that the product $K_{n, Λ}K_{m, Ω}$ of any two functions $K_{n, Λ}$ and $K_{m, Ω}$ from the family can be expressed as a linear combination of other functions from the family. In this paper, we show that this is indeed the case and that the span of the $K_{n, Λ}$'s forms an algebra. We also provide techniques for examining similar families of functions and a formula for the product $K_{n, Λ}K_{m, Ω}$ when $n=1$.
