论文标题
二进制形式和西尔维斯特定理的半不变
Semi-invariants of Binary Forms and Sylvester's Theorem
论文作者
论文摘要
我们获得了与二进制形式半不变的剪切转换有关的组合公式，这意味着在差分操作员方面，半不变的经典表征。然后，我们提出了希尔伯特（Hilbert）身份的组合证明，这导致了凯利（Cayley）在半不变性方面的关系。这种身份在与高斯系数有关的Sylvester定理的原始定理的原始证明中起着至关重要的作用。此外，我们表明，PAK和PANOVA的添加性引理可以从$ n，k \ geq 8 $上的高斯系数的严格单向性，可以从半非变量的环属性中得出。
We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in terms of a differential operator. Then, we present a combinatorial proof of an identity of Hilbert, which leads to a relation of Cayley on semi-invariants. This identity plays a crucial role in the original proof of Sylvester's theorem on semi-invariants in connection with the Gaussian coefficients. Moreover, we show that the additivity lemma of Pak and Panova which yields the strict unimodality of the Gaussian coefficients for $n,k \geq 8$ can be deduced from the ring property of semi-invariants.
