Haglund, Morse, and Zabrocki introduced a family of creation operators of Hall-Littlewood polynomials, \(\{C_{a}\}\) for any \(a\in \mathbb {Z}\) , in their compositional refinement of the shuffle (ex-)conjecture. For any \(\alpha \vDash n\) , the combinatorial formula for \(\nabla C_{\alpha }\) is a weighted sum of parking functions. These summations can be converted to a weighted sum of certain LLT polynomials. Thus, \(\nabla C_{\alpha }\) is Schur positive since Grojnowski and Haiman proved that all LLT polynomials are Schur positive. In this paper, we obtain a recursion that implies the C-positivity of \((-1)^{k} m_{2^{k}1^{l}}\) , and hence prove the Schur positivity of \((-1)^{k}\nabla m_{2^{k}1^{l}}\) . As a corollary, a parking function interpretation for \((-1)^{k}\nabla m_{2^{k}1^{l}}\) is obtained by using the compositional shuffle theorem of Carlsson and Mellit.
