Blossoms

[David Richardson]

So when I was studying I tried looking up a little information on
blossoms since the Agoston book doesn't provide a lot of basic
material on them.

The definition he gives (pg. 419) is:

Express p(u) in the form

p(u) = Sigma( i, 0, d, a^bar_i * ( d \ i ) * u^i )

The the blossom is:

P(u_1,u_2, ..., u_d) = Sigma( i, 0, d, a^bar_i * sigma_i(u_1,u_2, ...,
u_d) )

where sigma_i is the i-th elementary symmetric polynomial in u1_,
u_2, ..., u_d.

I was trying to find out how to form the elementary symmetric
polynomials. For the first few degrees it seems simple. Is it the case
that the i-th elementary symmetric polynomial is just the sum over of
products of elements of every i-sized subset of the set [k] =
{1,2, ...,k}?

Dave

[Chris Pollett]

>
>
> I was trying to find out how to form the elementary symmetric
> polynomials. For the first few degrees it seems simple. Is it the case
> that the i-th elementary symmetric polynomial is just the sum over of
> products of elements of every i-sized subset of the set [k] =
> {1,2, ...,k}?

Yes. That equation corresponds to the defining equation for blossoms in Buss.

Chris