2012
DOI: 10.1016/j.disc.2011.08.032
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Face vectors of subdivided simplicial complexes

Abstract: Brenti and Welker have shown that for any simplicial complex X, the face vectors of successive barycentric subdivisions of X have roots which converge to fixed values depending only on the dimension of X. We improve and generalize this result here. We begin with an alternative proof based on geometric intuition. We then prove an interesting symmetry of these roots about the real number -2. This symmetry can be seen via a nice algebraic realization of barycentric subdivision as a simple map on formal power seri… Show more

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Cited by 14 publications
(31 citation statements)
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“…Note that the coefficients λ i,j of Λ can be computed. We recall their values obtained in [3] in the following proposition and suggest an alternative proof.…”
Section: The Asymptotic Face Polynomialmentioning
confidence: 95%
See 4 more Smart Citations
“…Note that the coefficients λ i,j of Λ can be computed. We recall their values obtained in [3] in the following proposition and suggest an alternative proof.…”
Section: The Asymptotic Face Polynomialmentioning
confidence: 95%
“…We deduce from [2], [3] that the vector (q p,n ) 0≤p≤n is the eigenvector of Λ t n associated to the eigenvalue λ n+1,n+1 = (n + 1)! normalized by the relation q n,n = 1.…”
Section: The Asymptotic Face Polynomialmentioning
confidence: 98%
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