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Results tagged with polynomials
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user 490264
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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Abstract algebraic link between two problems involving polynomials and (generalized) Vanderm...
When studying the theory of splines, I came across the following Proposition: the family of polynomials
$$\Big\{\binom{N}{j} (X+\alpha_i)^{N-j}\Big\}_{i=0\dots L,\; j=0\dots k_i}$$
is always free (and … For example : could we prove the second proposition (show that the given family of polynomials is always free) simply by casting it into some form of generalized Hermite interpolation problem ? …
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Abstract algebraic link between two problems involving polynomials and (generalized) Vanderm...
Well, after some more thinking I'm going to answer my own question. It was pretty much just a matter of linking all elements together.
Here are my notations, in $\mathbb R_N[X]$.
Note $\partial$ the …