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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.
4
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When is a monic integer polynomial the characteristic polynomial of a non-negative integer m...
This is an interesting question! It seems that the corresponding problem even with "integer" replaced by "real" is hard (see Thomas J. Laffey, Inverse Eigenvalue Problems for Matrices, JSTOR), i.e., …