On Signed Multiplicities of Schur Expansions Surrounding Petrie Symmetric Functions

Yen-Jen Cheng, Meng-Chien Chou, Sen-Peng Eu +2

For $k\ge 1$, the homogeneous symmetric functions $G(k,m)$ of degree $m$ defined by ${\sum }_{m\ge 0}G(k,m)z^m={\prod }_{i\ge 1}(1+x_{i}z+x_i^2{z}^2+\cdots +x_i^{k-1}{z}^{k-1})$ are…