[seqfan] Re: Number of hierarchical polynomial models on n factors

viallon at math.univ-lyon1.fr viallon at math.univ-lyon1.fr
Wed Feb 8 21:53:36 CET 2012

Dear all,

just to confirm that my problem is exactly the one described by Neil.

It would be awesome if someone could find the formula!

Thanks in advance for your time!



"N. J. A. Sloane" <njas at research.att.com> a écrit :

> Paul, I think the question is the following:
> We are counting polynomials in n variables x_1 thru x_n
> The total degree is bounded by k (say)
> We don't care what the coeffients are
> All we care about is that if the
> polynomial contains a monomial
> x_1^e_1*x_2^e_2*...*x_n^e_n,
> then it also contains every monomial
> x_1^i_1*x_2^i_2*...*x_n^i_n
> for all 0 <= i_j <= e_j
> It should not be hard to work out a formula
> as a function of k and n
> Neil

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