The topology of the matching complex for the 2×n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(Δm n) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(Δm n). Furthermore, we determine the Euler characteristic of Ind(Δm n) and prove that several homology groups of Ind(Δm n) are non-zero.
|Journal||Electronic Journal of Combinatorics|
|State||Published - Oct 20 2017|
Bibliographical noteFunding Information:
Partially supported by grant H98230-16-1-0045 from the U.S. National Security Agency.
∗Partially supported by grant H98230-16-1-0045 from the U.S. National Security Agency.
© 2017, Australian National University. All rights reserved.
- Grid graphs
- Independence complexes
ASJC Scopus subject areas
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics