Jumps of Milnor Numbers of Brieskorn–Pham Singularities in Non-degenerate Families

The jump of the Milnor number of an isolated singularity $f_0$ is the minimal non-zero difference between the Milnor numbers of $f_0$ and one of its deformation $\left(f_s\right).$ In the case $f_s$ are non-degenerate singularities we call the jump non-degenerate. We give a formula (an inductive algorithm using diophantine equations) for the non-degenerate jump of $f_0$ in the case $f_0$ is a convenient singularity with only one $(n-1)$-dimensional face of its Newton diagram which equivalently (in our problem) can be replaced by the Brieskorn–Pham singularities.