# The Polytope of m-Subspaces of a Finite Affine Space

Julie Christophe; Jean-Paul Doignon

RAIRO - Operations Research (2007)

- Volume: 41, Issue: 3, page 317-344
- ISSN: 0399-0559

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topChristophe, Julie, and Doignon, Jean-Paul. "The Polytope of m-Subspaces of a Finite Affine Space." RAIRO - Operations Research 41.3 (2007): 317-344. <http://eudml.org/doc/250126>.

@article{Christophe2007,

abstract = {
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of
a finite affine space. The particular case of the hyperplane polytope
has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.
},

author = {Christophe, Julie, Doignon, Jean-Paul},

journal = {RAIRO - Operations Research},

keywords = {Convex polytope; finite affine space; m-subspace polytope; convex polytope; -subspace polytope},

language = {eng},

month = {8},

number = {3},

pages = {317-344},

publisher = {EDP Sciences},

title = {The Polytope of m-Subspaces of a Finite Affine Space},

url = {http://eudml.org/doc/250126},

volume = {41},

year = {2007},

}

TY - JOUR

AU - Christophe, Julie

AU - Doignon, Jean-Paul

TI - The Polytope of m-Subspaces of a Finite Affine Space

JO - RAIRO - Operations Research

DA - 2007/8//

PB - EDP Sciences

VL - 41

IS - 3

SP - 317

EP - 344

AB -
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of
a finite affine space. The particular case of the hyperplane polytope
has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.

LA - eng

KW - Convex polytope; finite affine space; m-subspace polytope; convex polytope; -subspace polytope

UR - http://eudml.org/doc/250126

ER -

## References

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