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- W2020473005 abstract "Let (an)n⩾0 be a sequence of complex numbers such that its generating series satisfies ∑n⩾0antn=h(t)(1−t)d for some polynomial h(t). For any r⩾1 we study the transformation of the coefficient series of h(t) to that of h〈r〉(t) where ∑n⩾0anrtn=h〈r〉(t)(1−t)d. We give a precise description of this transformation and show that under some natural mild hypotheses the roots of h〈r〉(t) converge when r goes to infinity. In particular, this holds if ∑n⩾0antn is the Hilbert series of a standard graded k-algebra A. If in addition A is Cohen–Macaulay then the coefficients of h〈r〉(t) are monotonically increasing with r. If A is the Stanley–Reisner ring of a simplicial complex Δ then this relates to the rth edgewise subdivision of Δ—a subdivision operation relevant in computational geometry and graphics—which in turn allows some corollaries on the behavior of the respective f-vectors." @default.
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- W2020473005 date "2009-05-01" @default.
- W2020473005 modified "2023-10-16" @default.
- W2020473005 title "The Veronese construction for formal power series and graded algebras" @default.
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- W2020473005 doi "https://doi.org/10.1016/j.aam.2009.01.001" @default.
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