On the number of faces of centrally-symmetric simplicial polytopes
نویسنده
چکیده
I. Bfirfiny and L. Lovfisz [Acta Math. Acad. Sci. Hung. 40, 323-329 (1982)] showed that a d-dimensional centrally-symmetric simplicial polytope ~ has at least 2 d facets, and conjectured a lower bound for the number f~ of i-dimensional faces o f ~ in terms ofd and the number f0 = 2n of d vertices. Define integers ho . . . . . he by Z f~-1(x 1) d-' = ~ hi xd-'. A. Bj6rner conjectured (uni=O i=O pub~ished) that hi > (di) (whi~ genera~ize~ the re~u~t ~f B~r~ny~L~v~ since f~-~ = ~ hi), and m°restr°nglythath~-hH>(di)-(i d_.l) l<i<[d/2J , _ _ conjecture of Bfirfiny-Lovfisz. In this paper the conjectures of Bj6rner are proved.
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عنوان ژورنال:
- Graphs and Combinatorics
دوره 3 شماره
صفحات -
تاریخ انتشار 1987