Mathematics – Combinatorics
Scientific paper
2011-02-15
Mathematics
Combinatorics
Improved exposition. 24 pages, 2 figures, 1 table
Scientific paper
Let X be a finite set of cardinality n. The Kalmanson complex K_n is the simplicial complex whose vertices are non-trivial X-splits, and whose facets are maximal circular split systems over X. In this paper we examine K_n from three perspectives. In addition to the T-theoretic description, we show that K_n has a geometric realization as the Kalmanson conditions on a finite metric. A third description arises in terms of binary matrices which possess the circular ones property. We prove the equivalence of these three definitions. This leads to a simplified proof of the well-known equivalence between Kalmanson and circular decomposable metrics, as well as a partial description of the f-vector of K_n.
Terhorst Jonathan
No associations
LandOfFree
The Kalmanson Complex does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Kalmanson Complex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Kalmanson Complex will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-416167