  In [7] we obtained a formula for the Hilbert depth of squarefree Veronese
ideals in a standard graded polynomial ring by relating it to the Hilbert depth
of powers of the irrelevant maximal ideal. In this paper, we prove that these
two Hilbert depth formulas are equivalent to each other. Our result reveals
that there is a strong connection between these two classes of seemingly
unrelated monomial ideals. We conjecture that their Stanley depths are
equivalent as well.
