Back to Search
Start Over
On the Homeomorphism and Homotopy Type of Complexes of Multichains.
- Source :
-
Annals of Combinatorics . Jun2023, Vol. 27 Issue 2, p229-247. 19p. - Publication Year :
- 2023
-
Abstract
- In this paper we define and study for a finite partially ordered set P a class of simplicial complexes on the set P r of r-element multichains of P. The simplicial complexes depend on a strictly monotone function from [r] to [2r]. We show that there are exactly 2 r such functions which yield subdivisions of the order complex of P, of which 2 r - 1 are pairwise different. Within this class are, for example, the order complexes of the intervals in P, the zig-zag poset of P, and the r th edgewise subdivision of the order complex of P. We also exhibit a large subclass for which our simplicial complexes are order complexes and homotopy equivalent to the order complex of P. [ABSTRACT FROM AUTHOR]
- Subjects :
- *PARTIALLY ordered sets
*SUBDIVISION surfaces (Geometry)
*HOMOTOPY equivalences
Subjects
Details
- Language :
- English
- ISSN :
- 02180006
- Volume :
- 27
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Annals of Combinatorics
- Publication Type :
- Academic Journal
- Accession number :
- 164228028
- Full Text :
- https://doi.org/10.1007/s00026-022-00626-y