Abstract
We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes, such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove Δ(K ∪ L) = Δ(Δ(K) ∪ Δ(L)) (conjectured by Kalai [6]), and for the join we give an example of simplicial complexes K and L for which Δ(K*L) ≠ Δ(Δ(K) *Δ(L)) (disproving a conjecture by Kalai [6]), where Δ denotes the (exterior) algebraic shifting operator. We develop a 'homological' point of view on algebraic shifting which is used throughout this work.
Original language | English |
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Pages (from-to) | 411-433 |
Number of pages | 23 |
Journal | Journal of Algebraic Combinatorics |
Volume | 22 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 2005 |
Externally published | Yes |
Keywords
- Algebraic shifting
- Simplicial complexes
ASJC Scopus subject areas
- Algebra and Number Theory
- Discrete Mathematics and Combinatorics