Schur超多项式：组合定义与Pieri法则
Schur Superpolynomials: Combinatorial Definition and Pieri Rule
摘要：
Schur超多项式最近被引入作为Macdonald超多项式的极限情况。证明了Schur多项式存在两个自然超扩张：在极限$q=t=0$和$q=t\rightarrow\infty$，分别对应于Schur超多项式及其对偶.然而，缺少直接的定义。在这里，我们提出了一个结构组合的定义，他们两个，每一个制定的一个独特的扩展半标准tableaux。这两个公式由另一个数学结果联系在一起，即舒尔超多项式的皮耶里规则。事实上，这是一个有趣的新奇的超级情况下，连续插入行由这个皮耶里规则不产生tableaux背后的舒尔超多项式组合结构，而是那些属于他们的双重版本。作为一个旁白，我们提出了各种扩展的舒尔双线性恒等式。
英文摘要：
Schur superpolynomials have been introduced recently as limiting cases of the Macdonald superpolynomials. It turns out that there are two natural super-extensions of the Schur polynomials: in the limit $q=t=0$ and $q=t\rightarrow\infty$, corresponding respectively to the Schur superpolynomials and their dual. However, a direct definition is missing. Here, we present a conjectural combinatorial definition for both of them, each being formulated in terms of a distinct extension of semi-standard tableaux. These two formulations are linked by another conjectural result, the Pieri rule for the Schur superpolynomials. Indeed, and this is an interesting novelty of the super case, the successive insertions of rows governed by this Pieri rule do not generate the tableaux underlying the Schur superpolynomials combinatorial construction, but rather those pertaining to their dual versions. As an aside, we present various extensions of the Schur bilinear identity.
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