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Results tagged with hilbert-function
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user 9025
For questions on the Hilbert function and Hilbert polynomial of graded algebras over fields.
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On the polynomial $\sum_{k=0}^n\binom{n}{k}(-1)^kX^{k(n-k)}$
The divisibility is easy to prove and a more general phenomenon. Let $Y=1-X$, then
$$F_n(X) = \sum_{k=0}^n (-1)^k \binom nk (1-Y)^{k(n-k)}=\sum_{r\ge 0} (-1)^r a_{r,n}Y^r$$ where $$a_{r,n} = \sum_{k= …
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