I certify that all formulas in the sections "A Combinatorial Interlude", "Back to inv-maj" and "Nice conjectures but what about proofs?" are correct. However I had some difficulties during my reading of the paper. It would be better if the authors provide more details.

1. Section "Guessing Polynomial Expressions for the Factorial Moments". The four conjectured expressions must have more leading terms, which will include all terms n^a*i^b such that a+b is maximal. The "degree" in (lower-degree-terms-in-(n,i)) must be the total degree. In the present form, we can't put i=n as required later in (Gnn').

2. Section "Nice conjectures but what about proofs?".
Why a lower-order-term is necessary a lower-degree-term-in-(n,i) ?
It seems not trivial, since a lower-order-term has the following form:

coeff(n) * FM(r',s')(n, i)

3. Page 6, line -6. Talking "leading terms of the FM's and the Mom's" means that FM and Mom are polynomials in n. It seems not trivial.

Some typos:

- FM[a1,...,ar] in page 6 and FM(r,s) in page 7. "()" or "[]" ?
- page 8, while the implication of Gnn is. Add "()" to Gnn
- page 9, La Grande Finale. "o" or "O" ?

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