We show that the coefficients of the representing polynomial of any monotone Boolean function are the values of a M\"obius function of an atomistic lattice related to this function. Using this we determine the representing polynomial of any Boolean function corresponding to a ST-CONNECTIVITY problem in acyclic quivers (directed acyclic multigraphs). Only monomials corresponding to unions of paths have non-zero coefficients which are $(-1)^D$ where $D$ is an easily computable function of the quiver corresponding to the monomial (it is the number of plane regions in the case of planar graphs). We estimate the number of monomials with non-zero coefficients for the two-dimensional grid connectivity problem as being between $\Omega(1.641^{2n^2})$ and $O(1.654^{2n^2})$.

翻译：我们显示,代表任何单质波列函数的多元波列函数的系数是与此函数相关的原子阵列的 M\ “ obius 函数的值。 使用这个系数, 我们就可以确定与环状孔径( 定向环状多幅图) 中ST- COONECTIVY 问题相对应的任何波列函数的多元值。 只有与路径组合相对应的单质波列函数的非零系数为$( 1)D$, 其中, 美元是单质方形( 平面图中的平面区域数) 的容易计算函数。 我们估计, 双维网状连接问题中带有非零系数的单体数在$\Omega( 41 ⁇ 2n ⁇ 2} $和$O( 1.654 ⁇ 2n) 美元之间。