934 research outputs found
The Extremal Structure Of Locally Compact Convex Sets
Let X be a locally compact closed convex subset of a locally convex Hausdorff topological linear space E. Then every exposed point of X is strongly exposed. The definitions of denting (strongly extreme) ray and strongly exposed ray are given for convex subsets of E. If X does not contain a line, then every extreme ray is strongly extreme and every exposed ray is strongly exposed. An example is given to show that the hypothesis that X be locally compact is necessary in both cases. © 1976 Pacific Journal of Mathematics. All rights reserved
Linear inequalities for flags in graded posets
The closure of the convex cone generated by all flag -vectors of graded
posets is shown to be polyhedral. In particular, we give the facet inequalities
to the polar cone of all nonnegative chain-enumeration functionals on this
class of posets. These are in one-to-one correspondence with antichains of
intervals on the set of ranks and thus are counted by Catalan numbers.
Furthermore, we prove that the convolution operation introduced by Kalai
assigns extreme rays to pairs of extreme rays in most cases. We describe the
strongest possible inequalities for graded posets of rank at most 5
Polyhedral Combinatorics of UPGMA Cones
Distance-based methods such as UPGMA (Unweighted Pair Group Method with
Arithmetic Mean) continue to play a significant role in phylogenetic research.
We use polyhedral combinatorics to analyze the natural subdivision of the
positive orthant induced by classifying the input vectors according to tree
topologies returned by the algorithm. The partition lattice informs the study
of UPGMA trees. We give a closed form for the extreme rays of UPGMA cones on n
taxa, and compute the normalized volumes of the UPGMA cones for small n.
Keywords: phylogenetic trees, polyhedral combinatorics, partition lattic
Promotion on Generalized Oscillating Tableaux and Web Rotation
We introduce the notion of a generalized oscillating tableau and define a
promotion operation on such tableaux that generalizes the classical promotion
operation on standard Young tableaux. As our main application, we show that
this promotion corresponds to rotation of the irreducible -webs of G.
Kuperberg.Comment: Comments welcom
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