On the Structure and Invariants of Cubical Complexes
1 online resource (124 pages) : PDF
University of North Carolina at Charlotte
This dissertation introduces two new results for cubical complexes. The first is a simple statistic on noncrossing partitions that expresses each coordinate of the toric h-vector of a cubical complex, written in the basis of the Adin h-vector entries, as the total weight of all noncrossing partitions. This expression can then be used to obtain a simple combinatorial interpretation of the contribution of a cubical shelling component to the toric h-vector. Secondly, a class of indecomposable permutations, bijectively equivalent to standard double occurrence words, may be used to encode one representative from each equivalence class of the shellings of the boundary of the hypercube. Finally, an adjacent transposition Gray code is constructed for this class of permutations, which can be implemented in constant amortized time.
COMBINATORICSCUBICAL COMPLEXGRAY CODEH-VECTORNONCROSSING PARTITIONSHELLING
Lucas, ThomasHouston, EvanDiao, YuananCooper, W. Douglas
Thesis (Ph.D.)--University of North Carolina at Charlotte, 2013.
This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). For additional information, see http://rightsstatements.org/page/InC/1.0/.
Copyright is held by the author unless otherwise indicated.