Abstract
In this paper, we present some work towards a complete characterization of Hilbert quasi-polynomials of graded polynomial rings. In this setting, a Hilbert quasi-polynomial splits in a polynomial F and a lower degree quasi-polynomial G. We completely describe the periodic structure of G. Moreover, we give an explicit formula for the \((n-1)\)th and \((n-2)\)th coefficient of F, where n denotes the degree of F. Finally, we provide an algorithm to compute the Hilbert quasi-polynomial of any graded polynomial ring.
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Caboara, M., Mascia, C. A partial characterization of Hilbert quasi-polynomials in the non-standard case. AAECC 33, 3–20 (2022). https://doi.org/10.1007/s00200-020-00423-1
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DOI: https://doi.org/10.1007/s00200-020-00423-1