Matching and Independence Complexes Related to Small Grids

Authors

Benjamin Braun, University of KentuckyFollow
Wesley K. Hough, University of Wisconsin - Whitewater

Abstract

The topology of the matching complex for the 2 x n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(Δ^m_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(Δ^m_n). Furthermore, we determine the Euler characteristic of Ind(Δ^m_n) and prove that several homology groups of Ind(Δ^m_n) are non-zero.

Document Type

Article

Publication Date

10-20-2017

Notes/Citation Information

Published in The Electronic Journal of Combinatorics, v. 24, issue 4, paper #P4.18, p. 1-20.

The publisher has granted the permission for posting the article here.

Funding Information

Benjamin Braun partially supported by grant H98230-16-1-0045 from the U.S. National Security Agency.

Repository Citation

Braun, Benjamin and Hough, Wesley K., "Matching and Independence Complexes Related to Small Grids" (2017). Mathematics Faculty Publications. 26.
https://uknowledge.uky.edu/math_facpub/26