doesn’t contain $x_{\gamma}(-1)$ elements or is of the form:\
    $x(\pi) = \dots (-j)x_{\gamma}(-1)$,  $j \geq 2$ for $\gamma \in \{\gamma_{\ell}, \gamma_{\underline{\ell-1}}, \dots, \gamma_{\underline{2}} \}$,

-   for $\Lambda = {\Lambda_{\ell}}$, a monomial $x(\pi)$ satisfies the initial conditions if it either doesn’t contain $x_{\gamma}(-1)$ elements or is of the form:\
    $x(\pi) = \dots (-j)x_{\gamma}(-1)$,  $j \geq 2$ for $\gamma \in \{\gamma_{\underline{\ell}}, \gamma_{\underline{\ell-1}}, \dots, \gamma_{\underline{2}} \}$,

-   for $\Lambda = \Lambda_1$, a monomial $x(\pi)$ satisfies the initial conditions if it doesn’t contain $x_{\gamma}(-1)$ elements.

Those conditions can be also expressed using inequalities. Let $b_{i}$ denote the number of $x_{\gamma_i}(-1)$ factors in the monomial $x(\pi)$ and $b_{\underline{i}}$ the number of $x_{\gamma_{\underline{i}}}(-1)$ factors. Then $x(\pi)$ satisfies the initial conditions if:

-   on $v_{\Lambda_0}$:

    -   $b_{\underline{3}} \dots + b_{\underline{\ell}} + b_{\ell} +
        \dots + b_2  \leq 1$,

    -   $b_{\underline{2}} + b_{\underline{3}} \dots +
        b_{\underline{\ell}} + b_{\ell} + \dots + b_{3}  \leq 1$,

-   on $v_{\Lambda_{\ell-1}}$:

    -   $b_{\underline{\ell}} + b_{\ell-1} + b_{\ell-2} + \dots + b_2 \leq 0 $,

    -   $b_\ell + b_{\ell-1} +
        \dots + b_2  \leq 1$,

    -   $b_{\underline{2}} + \dots +
        b_{\underline{\ell}} + b_{\ell} + \dots + b_{3}  \leq 1$,

-   on $v_{\Lambda_l}$:

    -   $b_\ell + b_{\ell-1} + b_{\ell-2} + \dots + b_2 \leq 