论文标题
通过晶格路径进行标记的多项式二元性
Flagged Schur polynomial duality via a lattice path bijection
论文作者
论文摘要
本文证明了标记的Schur多项式之间的身份，在行标志和列标志之间给出了二元性。这种身份概括了由于gessel和viennot引起的二项式决定偶性定理，以及由于aitken引起的对称函数二元性定理。作为推论，我们获得了二项式决定偶发性定理的升力，为$ q $ binmial系数和对称多项式。我们的方法是对Gessel和Viennot使用的新型晶格概括的路径计数。
This paper proves an identity between flagged Schur polynomials, giving a duality between row flags and column flags. This identity generalises both the binomial determinant duality theorem due to Gessel and Viennot and the symmetric function duality theorem due to Aitken. As corollaries we obtain the lifts of the binomial determinant duality theorem to $q$-binomial coefficients and to symmetric polynomials. Our method is a path counting argument on a novel lattice generalising that used by Gessel and Viennot.
