Geodesic
The topology of the external activity complex of a matroid
Federico Ardila1 ; Federico Castillo2 ; José Alejandro Samper3
1San Francisto State University
2University of California, Davis.
3University of Washington
The electronic journal of combinatorics, Tome 23 (2016) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We prove that the external activity complex $\textrm{Act}_<(M)$ of a matroid is shellable. In fact, we show that every linear extension of LasVergnas's external/internal order $<_{ext/int}$ on $M$ provides a shelling of $\textrm{Act}_<(M)$. We also show that every linear extension of LasVergnas's internal order $<_{int}$ on $M$ provides a shelling of the independence complex $IN(M)$. As a corollary, $\textrm{Act}_<(M)$ and $M$ have the same $h$-vector. We prove that, after removing its cone points, the external activity complex is contractible if $M$ contains $U_{1,3}$ as a minor, and a sphere otherwise.
DOI : 10.37236/5042
Classification : 05B35, 52B40
Mots-clés : matroid theory, shellability, linear extensions

Federico Ardila  1   ; Federico Castillo  2   ; José Alejandro Samper  3

1 San Francisto State University
2 University of California, Davis.
3 University of Washington 
@article{10_37236_5042,
     author = {Federico Ardila and Federico Castillo and Jos\'e Alejandro Samper},
     title = {The topology of the external activity complex of a matroid},
     journal = {The electronic journal of combinatorics},
     year = {2016},
     volume = {23},
     number = {3},
     doi = {10.37236/5042},
     zbl = {1344.05036},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/5042/}
}
TY  - JOUR
AU  - Federico Ardila
AU  - Federico Castillo
AU  - José Alejandro Samper
TI  - The topology of the external activity complex of a matroid
JO  - The electronic journal of combinatorics
PY  - 2016
VL  - 23
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/5042/
DO  - 10.37236/5042
ID  - 10_37236_5042
ER  - 
%0 Journal Article
%A Federico Ardila
%A Federico Castillo
%A José Alejandro Samper
%T The topology of the external activity complex of a matroid
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5042/
%R 10.37236/5042
%F 10_37236_5042
Federico Ardila; Federico Castillo; José Alejandro Samper. The topology of the external activity complex of a matroid. The electronic journal of combinatorics, Tome 23 (2016) no. 3. doi: 10.37236/5042

Cité par Sources :