Bounds on the $f$-Vectors of Tight Spans

Details Bounds on the $f$-Vectors of Tight Spans Bounds on the $f$-Vectors of Tight Spans

2006-05-15

arxiv.org/abs/math/0605401v1

Mathematics

Metric Geometry

18 pages

Scientific paper

The tight span $T_d$ of a metric $d$ on a finite set is the subcomplex of
bounded faces of an unbounded polyhedron defined by~$d$. If $d$ is generic then
$T_d$ is known to be dual to a regular triangulation of a second hypersimplex.
A tight upper and a partial lower bound for the face numbers of $T_d$ (or the
dual regular triangulation) are presented.

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