Geodesic
Topological representations of matroids
Swartz, E.1
1 Malott Hall, Cornell University, Ithaca, New York 14853
Journal of the American Mathematical Society, Tome 16 (2003) no. 2, pp. 427-442

Voir la notice de l'article provenant de la source American Mathematical Society

There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky’s enumeration of the cells of the arrangement still holds. Bounded subcomplexes of an arrangement of homotopy spheres correspond to minimal cellular resolutions of the dual matroid Steiner ideal. As a result, the Betti numbers of the ideal are computed and seen to be equivalent to Stanley’s formula in the special case of face ideals of independence complexes of matroids.
DOI : 10.1090/S0894-0347-02-00413-7

Swartz, E. 1

1 Malott Hall, Cornell University, Ithaca, New York 14853 
@article{10_1090_S0894_0347_02_00413_7,
     author = {Swartz, E.},
     title = {Topological representations of matroids},
     journal = {Journal of the American Mathematical Society},
     pages = {427--442},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2003},
     doi = {10.1090/S0894-0347-02-00413-7},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-02-00413-7/}
}
TY  - JOUR
AU  - Swartz, E.
TI  - Topological representations of matroids
JO  - Journal of the American Mathematical Society
PY  - 2003
SP  - 427
EP  - 442
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-02-00413-7/
DO  - 10.1090/S0894-0347-02-00413-7
ID  - 10_1090_S0894_0347_02_00413_7
ER  - 
%0 Journal Article
%A Swartz, E.
%T Topological representations of matroids
%J Journal of the American Mathematical Society
%D 2003
%P 427-442
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-02-00413-7/
%R 10.1090/S0894-0347-02-00413-7
%F 10_1090_S0894_0347_02_00413_7
Swartz, E. Topological representations of matroids. Journal of the American Mathematical Society, Tome 16 (2003) no. 2, pp. 427-442. doi: 10.1090/S0894-0347-02-00413-7

[1] Bayer, Dave, Sturmfels, Bernd Cellular resolutions of monomial modules J. Reine Angew. Math. 1998 123 140

[2] Bayer, Margaret, Sturmfels, Bernd Lawrence polytopes Canad. J. Math. 1990 62 79

[3] Bjã¶Rner, Anders, Las Vergnas, Michel, Sturmfels, Bernd, White, Neil, Ziegler, Gã¼Nter M. Oriented matroids 1999

[4] Losinsky, S. Sur le procédé d’interpolation de Fejér C. R. (Doklady) Acad. Sci. URSS (N.S.) 1939 318 321

[5] Colbourn, Charles J., Pulleyblank, William R. Matroid Steiner problems, the Tutte polynomial and network reliability J. Combin. Theory Ser. B 1989 20 31

[6] Crapo, Henry H. A higher invariant for matroids J. Combinatorial Theory 1967 406 417

[7] Folkman, Jon The homology groups of a lattice J. Math. Mech. 1966 631 636

[8] Folkman, Jon, Lawrence, Jim Oriented matroids J. Combin. Theory Ser. B 1978 199 236

[9] Mcnulty, Jennifer Generalized affine matroids Congr. Numer. 1994 243 254

[10] Oxley, James G. Matroid theory 1992

[11] Spanier, Edwin H. Algebraic topology 1966

[12] Stanley, Richard P. Cohen-Macaulay complexes 1977 51 62

[13] Wachs, Michelle L., Walker, James W. On geometric semilattices Order 1986 367 385

[14] Zaslavsky, Thomas Facing up to arrangements: face-count formulas for partitions of space by hyperplanes Mem. Amer. Math. Soc. 1975

[15] Zaslavsky, Thomas A combinatorial analysis of topological dissections Advances in Math. 1977 267 285

[16] Ziegler, Gã¼Nter M., ŽIvaljeviä‡, Rade T. Homotopy types of subspace arrangements via diagrams of spaces Math. Ann. 1993 527 548

Cité par Sources :