论文标题
$ k $ -kohnert图和反向设置值的tableaux之间的培训
A bijection between $K$-Kohnert diagrams and reverse set-valued tableaux
论文作者
论文摘要
Lascoux多项式是$ K $ - 关键多项式的理论类似物。他们俩都有涉及tableaux的组合公式：反向设置值tableaux（$ \ mathsf {rsvt} $）lascoux polyenmials的规则和反向semistandard Young tableaux（$ \ mathsf {rssyt} $）的关键多项式规则。此外，关键多项式具有一个简单的算法模型，而Kohnert图则与$ \ Mathsf {rssyt} $一起进行培养。罗斯（Ross）和杨（Yong）介绍了$ k $ -kohnert图，这是Kohnert图的类似物。他们猜想了Lascoux多项式的$ K $ -KOHNERT图规则。我们通过在$ \ mathsf {rsvt} $和$ k $ -kohnert图之间构建举重的两者来建立这种猜想。
Lascoux polynomials are $K$-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux ($\mathsf{RSVT}$) rule for Lascoux polynomials and reverse semistandard Young tableaux ($\mathsf{RSSYT}$) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with $\mathsf{RSSYT}$. Ross and Yong introduced $K$-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a $K$-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between $\mathsf{RSVT}$ and $K$-Kohnert diagrams.
