05280748

j

05280748 Herrmann, Sven Genocchi numbers and $f$-vectors of simplicial balls. Eur. J. Comb. 29, No. 5, 1087-1091 (2008). 2008 Elsevier Science (Academic Press), London EN Zbl 1081.52011 Zbl 1204.52013

doi:10.1016/j.ejc.2007.09.001

Summary: The Genocchi numbers $G_n$, $n\geq 0$ are the coefficients of the generating function $\frac {2t}{e^t +1}$. In this note we give an equation for simplicial balls which involves these numbers. It relates the number of faces in the interior of the ball to the number of faces in the boundary of the ball. This is a variation of similar equations given in [{\it P. McMullen}, Beitr. Algebra Geom. 45, No. 1, 37--46 (2004; Zbl 1081.52011); the author and {\it M. Joswig}, Contrib. Discrete Math. 2, No. 2, 161--184, electronic only (2007; Zbl 1204.52013), see also \url{arXiv:math.MG/0605401}].