Abstract
The flag vector contains all the face incidence data of a polytope, and in the poset setting, the chain enumerative data. It is a classical result due to Bayer and Klapper that for face lattices of polytopes, and more generally, Eulerian graded posets, the flag vector can be written as a cd-index, a non-commutative polynomial which removes all the linear redundancies among the flag vector entries. This result holds for regular CW complexes.We relax the regularity condition to show the cd-index exists for Whitney stratified manifolds by extending the notion of a graded poset to that of a quasi-graded poset. This is a poset endowed with an order-preserving rank function and a weighted zeta function. This allows us to generalize the classical notion of Eulerianness, and obtain a cd-index in the quasi-graded poset arena. We also extend the semi-suspension operation to that of embedding a complex in the boundary of a higher dimensional ball and study the simplicial shelling components.
Original language | English |
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Pages (from-to) | 85-128 |
Number of pages | 44 |
Journal | Advances in Mathematics |
Volume | 268 |
DOIs | |
State | Published - Jan 2 2015 |
Bibliographical note
Publisher Copyright:© 2014 Elsevier Inc.
Keywords
- Eulerian condition
- Primary
- Quasi-graded poset
- Secondary
- Semisuspension
- Weighted zeta function
- Whitney's conditions A and B
ASJC Scopus subject areas
- General Mathematics