Geodesic
Face numbers of centrally symmetric polytopes produced from Split graphs
Ragnar Freij1 ; Matthias Henze2 ; Moritz W. Schmitt3 ; Günter M. Ziegler3
1Department of Mathematics and Systems Analysis Aalto University Espoo, Finland
2Institut für Informatik Freie Universität Berlin Berlin, Germany
3Institut für Mathematik Freie Universität Berlin Berlin, Germany
The electronic journal of combinatorics, Tome 20 (2013) no. 2
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We analyze a remarkable class of centrally symmetric polytopes, the Hansen polytopes of split graphs. We confirm Kalai's $3^d$ conjecture for such polytopes (they all have at least $3^d$ nonempty faces) and show that the Hanner polytopes among them (which have exactly $3^d$ nonempty faces) correspond to threshold graphs. Our study produces a new family of Hansen polytopes that have only $3^d+16$ nonempty faces.
DOI : 10.37236/3315
Classification : 52B05, 52B12, 05C75
Mots-clés : Hansen polytopes, Hanner polytopes, split graphs, threshold graphs, centrally symmetric polytopes, Kalai's \(3^d\) conjecture

Ragnar Freij  1   ; Matthias Henze  2   ; Moritz W. Schmitt  3   ; Günter M. Ziegler  3

1 Department of Mathematics and Systems Analysis Aalto University Espoo, Finland
2 Institut für Informatik Freie Universität Berlin Berlin, Germany
3 Institut für Mathematik Freie Universität Berlin Berlin, Germany 
@article{10_37236_3315,
     author = {Ragnar Freij and Matthias Henze and Moritz W. Schmitt and G\"unter M. Ziegler},
     title = {Face numbers of centrally symmetric polytopes produced from {Split} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2013},
     volume = {20},
     number = {2},
     doi = {10.37236/3315},
     zbl = {1270.52011},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/3315/}
}
TY  - JOUR
AU  - Ragnar Freij
AU  - Matthias Henze
AU  - Moritz W. Schmitt
AU  - Günter M. Ziegler
TI  - Face numbers of centrally symmetric polytopes produced from Split graphs
JO  - The electronic journal of combinatorics
PY  - 2013
VL  - 20
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.37236/3315/
DO  - 10.37236/3315
ID  - 10_37236_3315
ER  - 
%0 Journal Article
%A Ragnar Freij
%A Matthias Henze
%A Moritz W. Schmitt
%A Günter M. Ziegler
%T Face numbers of centrally symmetric polytopes produced from Split graphs
%J The electronic journal of combinatorics
%D 2013
%V 20
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3315/
%R 10.37236/3315
%F 10_37236_3315
Ragnar Freij; Matthias Henze; Moritz W. Schmitt; Günter M. Ziegler. Face numbers of centrally symmetric polytopes produced from Split graphs. The electronic journal of combinatorics, Tome 20 (2013) no. 2. doi: 10.37236/3315

Cité par Sources :