87,729 research outputs found
F-Vectors of barycentric subdivisions
No full textFor a simplicial complex or more generally Boolean cell complex Delta we study the behavior of the f- and h-vector under barycentric subdivision. We show that if Delta has a non-negative h-vector then the h-polynomial of its barycentric subdivision has only simple and real zeros. As a consequence this implies a strong version of the Charney-Davis conjecture for spheres that are the subdivision of a Boolean cell complex or the subdivision of the boundary complex of a simple polytope. For a general (d -1)-dimensional simplicial complex Delta the h-polynomial of its n-th iterated subdivision shows convergent behavior. More precisely, we show that among the zeros of this h-polynomial there is one converging to infinity and the other d -1 converge to a set of d - 1 real numbers which only depends on d
The Veronese construction for formal power series and graded algebras
No full textLet (a(n))(n >= 0) be a sequence of complex numbers such that its generating series satisfies Sigma(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 Sigma(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 Sigma(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 Lambda is the Stanley-Reisner ring of a simplicial complex Delta then this relates to the rth edgewise subdivision of Delta-a subdivision operation relevant in computational geometry and graphics-which in turn allows some corollaries on the behavior of the respective f-vectors. (c) 2009 Elsevier Inc. All rights reserved
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
The Cestos Reporter
No full textWeekly newspaper from Cestos, Oklahoma Territory that includes local, territorial, and United States national news along with advertising
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