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- W4294804912 abstract "Regarding non-unique factorization of integer-valued polynomials over a discrete valuation domain $(R,M)$ with finite residue field, it is known that there exist absolutely irreducible elements, that is, irreducible elements all of whose powers factor uniquely, and non-absolutely irreducible elements. We completely and constructively characterize the absolutely irreducible elements among split integer-valued polynomials. They correspond bijectively to finite sets, which we call emph{balanced}, characterized by a combinatorial property regarding the distribution of their elements among residue classes of powers of $M$. For each such balanced set as the set of roots of a split polynomial, there exists a unique vector of multiplicities and a unique constant so that the corresponding product of monic linear factors times the constant is an absolutely irreducible integer-valued polynomial. This also yields sufficient criteria for integer-valued polynomials over Dedekind domains to be absolutely irreducible." @default.
- W4294804912 created "2022-09-06" @default.
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- W4294804912 date "2021-07-29" @default.
- W4294804912 modified "2023-10-17" @default.
- W4294804912 title "Split absolutely irreducible integer-valued polynomials over discrete valuation domains" @default.
- W4294804912 doi "https://doi.org/10.48550/arxiv.2107.14276" @default.
- W4294804912 hasPublicationYear "2021" @default.
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