论文标题
提起双重完美的功能
Lifting the dual immaculate functions
论文作者
论文摘要
我们向多项式环引入了双色完美的准对称函数的两个升力。我们为这些双重完美的幻灯片多项式扩展到基本载玻片和准键基底座中，建立了积极的公式。这些公式反映了双重完美的准对称函数，基本的准对称函数和年轻的准对称Schur函数之间的连接，将这些连接从准对称函数环扩展到了完整的多项式环。我们还考虑了双色完美的准对称函数的反向变体，反映了准对称Schur函数与年轻的准对称Schur函数之间的二分法。我们表明，通过采取稳定限制我们的一个升力，并利用这些反式双色完美的准对称函数来获得这种变体，以在双重完美的准绝对准对称函数与多项元素的基础之间建立联系。
We introduce two lifts of the dual immaculate quasisymmetric functions to the polynomial ring. We establish positive formulas for expansions of these dual immaculate slide polynomials into the fundamental slide and quasi-key bases for polynomials. These formulas mirror connections between dual immaculate quasisymmetric functions, fundamental quasisymmetric functions, and Young quasisymmetric Schur functions, extending these connections from the ring of quasisymmetric functions to the full polynomial ring. We also consider a reverse variant of the dual immaculate quasisymmetric functions, mirroring the dichotomy between the quasisymmetric Schur functions and the Young quasisymmetric Schur functions. We show this variant is obtained by taking stable limits of one of our lifts, and utilize these reverse dual immaculate quasisymmetric functions to establish a connection between the dual immaculate quasisymmetric functions and the Demazure atom basis for polynomials.
