AI 中文总结
该研究分类了拟对称函数代数中双无瑕函数在对合ρ、ψ、ω作用下的相等情况，确定了过渡矩阵首项与无瑕表格存在的充要条件，发现了与分划相关的新映射和典范表格。
AI 中文摘要
双无瑕函数是拟对称函数代数中一类类似舒尔基的基。我们对在对合ρ、ψ、ω中某一个作用下双无瑕函数的像等于另一个双无瑕函数的情况进行分类，同时确定了过渡矩阵的首项，得出了存在无瑕表格的充要条件。由此，还发现了与分划相关的新映射和典范表格。
英文摘要
The dual immaculate functions are an example of a Schur-like basis in the algebra of quasisymmetric functions. We classify when the image of a dual immaculate function under one of the involutions $ρ, ψ, ω$ is equal to a dual immaculate function. As well, the leading term of the transition matrix is identified, and sufficient and necessary conditions for the existence of immaculate tableaux are determined. As a consequence, new maps and canonical tableaux associated with compositions are discovered.
Comments29 pages, 22 figures
