Bounds on the f-Vectors of Tight Spans

2006/05/15 by Sven Herrmann, Herrmann, Sven, Michael Joswig +1 · 2 citations
Computer Science · Engineering · Mathematics · #51K05 (52B05) #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #FOS: Mathematics #Metric Geometry (math.MG) #Polynomial and algebraic computation #math.MG #msc:51K05

paper · pdf · doi:10.48550/arxiv.math/0605401

18 pages

arxiv created 2006/05/15 · openalex publication_date 2006/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Computing the bounded subcomplex of an unbounded polyhedron
• Genocchi numbers and f-vectors of simplicial balls

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