In this work we introduce new combinatorial objects called d--fold
partition diamonds, which generalize both the classical partition function and
the partition diamonds of Andrews, Paule and Riese, and we set rdβ(n) to be
their counting function. We also consider the Schmidt type d--fold partition
diamonds, which have counting function sdβ(n). Using partition analysis, we
then find the generating function for both, and connect the generating
functions βn=0ββsdβ(n)qn to Eulerian polynomials. This allows
us to develop elementary proofs of infinitely many Ramanujan--like congruences
satisfied by sdβ(n) for various values of d, including the following
family: for all dβ₯1 and all nβ₯0,sdβ(2n+1)β‘0(mod2d).Comment: 16 pages, 3 figures; v2: added a new result concerning Eulerian
polynomials and several subsequent congruences for sdβ(n), and corrected
a mistake in the proof of Proposition 1.