We investigate chromatic symmetric functions in relation to the algebra \(\varGamma \) of symmetric functions generated by Schur Q-functions. We construct natural bases of \(\varGamma \) in terms of chromatic symmetric functions. We also consider the p-positivity of skew Schur Q-functions and find a class of p-positive ribbon Schur Q-functions, making a conjecture that they are only p-positive Schur Q-functions. We include many concrete computational results that support our conjecture.

中文翻译：

---

偏基Schur Q函数的色基和p-正性的类似物

我们研究与Schur Q函数生成的对称函数的代数\（\ varGamma \）有关的色对称函数。我们根据色对称函数构造\（\ varGamma \）的自然基础。我们还考虑了偏斜Schur Q函数的p正性，并找到了一类p正带状Schur Q函数，从而推测它们只是p正Schur Q函数。我们包括许多支持我们猜想的具体计算结果。