221 citations · 932 across the 42 of their papers we have counts for
8 papers · 1 filter
The maximum quartet distance between phylogenetic trees
Lior Pachter
The quartet distance counts the four-leaf subsets on which two binary phylogenetic trees display different topologies. We prove that its maximum over trees on leaves is $(2/3+o…
Optimal pebbling of the hypercube
Lior Pachter
We prove that the optimal pebbling number of the -dimensional hypercube is \[ o(Q_n)\,=\,Θ\!\left(\left(\frac43\right)^n\right). \]
Affine and Projective Tree Metric Theorems
Aaron Kleinman, Matan Harel, Lior Pachter
The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) f…
Selecting universities: personal preference and rankings
Peter Huggins, Lior Pachter
Polyhedral geometry can be used to quantitatively assess the dependence of rankings on personal preference, and provides a tool for both students and universities to assess US News…
Combinatorics of least squares trees
Radu Mihaescu, Lior Pachter
A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These for…
Convex Rank Tests and Semigraphoids
Jason Morton, Lior Pachter, Anne Shiu +2
Convex rank tests are partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutation…