%0 Journal Article %1 Fishburn1998 %A Fishburn, P. C. %A Trotter, W. T. %D 1998 %J Order %K geometric_containment_orders poset %N 2 %P 167--182 %R 10.1023/A:1006110326269 %T Geometric Containment Orders: A Survey %U https://doi.org/10.1023/A:1006110326269 %V 15 %X A partially ordered set (X, ≺) is a geometric containment order of a particular type if there is a mapping from X into similarly shaped objects in a finite-dimensional Euclidean space that preserves ≺ by proper inclusion. This survey describes most of what is presently known about geometric containment orders. Highlighted shapes include angular regions, convex polygons and circles in the plane, and spheres of all dimensions. Containment orders are also related to incidence orders for vertices, edges and faces of graphs, hypergraphs, planar graphs and convex polytopes. Three measures of poset complexity are featured: order dimension, crossing number, and degrees of freedom.

@article{Fishburn1998, abstract = {A partially ordered set (X, ≺) is a geometric containment order of a particular type if there is a mapping from X into similarly shaped objects in a finite-dimensional Euclidean space that preserves ≺ by proper inclusion. This survey describes most of what is presently known about geometric containment orders. Highlighted shapes include angular regions, convex polygons and circles in the plane, and spheres of all dimensions. Containment orders are also related to incidence orders for vertices, edges and faces of graphs, hypergraphs, planar graphs and convex polytopes. Three measures of poset complexity are featured: order dimension, crossing number, and degrees of freedom.}, added-at = {2024-04-26T19:31:54.000+0200}, author = {Fishburn, P. C. and Trotter, W. T.}, biburl = {https://www.bibsonomy.org/bibtex/2b3576374823499bd6822db546ab532f2/duerrschnabel}, day = 01, doi = {10.1023/A:1006110326269}, interhash = {72852610f889893279d8bca00782d704}, intrahash = {b3576374823499bd6822db546ab532f2}, issn = {1572-9273}, journal = {Order}, keywords = {geometric_containment_orders poset}, month = jun, number = 2, pages = {167--182}, timestamp = {2024-04-26T19:31:54.000+0200}, title = {Geometric Containment Orders: A Survey}, url = {https://doi.org/10.1023/A:1006110326269}, volume = 15, year = 1998 }