Opening book details…
Can I read The Veronese construction for formal power series and graded algebras on EtoBox?
The Veronese construction for formal power series and graded algebras by Francesco Brenti; Volkmar Welker is a Mathematics article available to read on EtoBox.
What is The Veronese construction for formal power series and graded algebras about?
## Real-rootedness Unimodality Edgewise subdivision Let (a n ) n 0 be a sequence of complex numbers such that its generating series satisfies n 0 a n t n = 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 0 a nr t n = 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 0 a n t n 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.
Who reads The Veronese construction for formal power series and graded algebras?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Francesco Brenti; Volkmar Welker
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0196-8858)
- Published
- 2009
- Language
- EN
- Field
- Mathematics (Physical Sciences)