Genocchi numbers and f-vectors of simplicial balls

2007/02/28 by Sven Herrmann
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Ball (mathematics) #Boundary (topology) #Combinatorics #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #math.CO #msc:11B83 #msc:52B05

paper · pdf · doi:10.1016/j.ejc.2007.09.001

published as European Journal of Combinatorics, 29 (2008), no. 5, 1087-109 · revised version, to appear in European Journal of Combinatorics; minor changes

arxiv created 2007/09/26 · openalex publication_date 2007/10/24 · arxiv updated 2014/12/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Genocchi numbers are the coefficients of the generating function 2t/(e^t+1). In this note we will give an equation for simplicial balls which involves this numbers. It relates the number of faces in the interior of the ball with the number of faces in the boundary of the ball. This is a variation of similar equations given in [McMullen 2004] and [Herrmann and Joswig 2006].

Citations

• Interprétations combinatoires des nombres de Genocchi
• Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
• Bounds on the f-Vectors of Tight Spans