  These notes are designed to offer some (perhaps new) codicils to related
work, a list of problems and conjectures seeking (preferably) combinatorial
proofs. The main items are Eulerian polynomials and hook/contents of Young
diagram, mostly on the latter. We also have items on Frobenius theorem and
multi-core partitions; most recently, some problems on (what we call) colored
over-partitions. Formulas analogues to or in the spirit of works by Han,
Nekrasov-Okounkov and Stanley are distributed throughout. Concluding remarks
are provided at the end in hopes of directing the interested researcher,
properly. The newly added problem is on chromatic polynomials
