Lower bounds for the \(cd\)-index of odd-dimensional simplicial manifolds
type: Item
instance of: scholarly article
title: Lower bounds for the \(cd\)-index of odd-dimensional simplicial manifolds
zbMATH Open document ID: 0960.52010
author: Isabella Novik
published in: European Journal of Combinatorics
publication date: 2000-08-28T00:00:00Z
review text: The \(cd\)-index was introduced by Fine [see \textit{M. M. Bayer} and \textit{A. Klapper}, Discrete Comput. Geom. 3, No. 1, 33-47 (1991; Zbl 0761.52009)], to encode the flag \(f\)-vector of an eulerian poset. \textit{R. P. Stanley} [Math. Z. 216, No. 3, 483-499 (1994; Zbl 0805.06003)] showed that the \(cd\)-index is non-negative for many classes of posets. Here, the author extends this to show that many of the coefficients of the \(cd\)-index of odd-dimensional simplicial manifolds are also non-negative.
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 1463386
zbMATH Keywords: simplicial manifold
zbMATH Keywords: \(cd\)-index
zbMATH Keywords: flag \(f\)-vector
zbMATH Keywords: eulerian poset
zbMATH Keywords: odd-dimensional
zbMATH Keywords: simplicial manifolds
reviewed by: Peter McMullen
MaRDI profile type: Publication
full work available at URL: eujc.1999.0352
OpenAlex ID: W2070001083
cites work: Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets
cites work: A new index for polytopes
cites work: Monotonicity of the cd-index for polytopes
cites work: An extended Euler-Poincaré theorem
cites work: Coproducts and the cd-index
cites work: Q4317713
cites work: On the \(cd\)-variation polynomials of André and Simsun permutations
cites work: Q3974981
cites work: A Combinatorial Analogue of Poincaré's Duality Theorem
cites work: Upper bound theorems for homology manifolds
cites work: On the number of faces of simplicial complexes and the purity of Frobenius
cites work: Flag \(f\)-vectors and the \(cd\)-index
cites work: Q4309966
cites work: Combinatorics and commutative algebra.
DOI: 10.1006/EUJC.1999.0352
description: scientific article; zbMATH DE number 1463386