Título inglés |
On the refinements of a polyhedral subdivision. |
Título español |
Refinamientos de una subdivisión poliedral. |
Autor/es |
Santos, Francisco |
Organización |
Dep. Mat. Estad. Comput. Univ. Cantabria, Santander, España |
Revista |
0010-0757 |
Publicación |
2001, 52 (3): 231-256, 26 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced subdivision. In particular, we define the refinement polytope associated to any pi-induced subdivision S, which is a generalization of the fiber polytope and shares most of its properties. As applications to the theory we prove that if a point configuration has non-regular subdivisions then it has non-regular triangulations and we provide simple proofs of the existence of non-regular subdivisions for many particular point configurations. |
Clasificación UNESCO |
120410 |
Palabras clave español |
Geometría proyectiva ; Politopos ; Refinamiento ; Poliedro |
Código MathReviews |
MR1885221 |
Código Z-Math |
Zbl 1012.52018 |
Acceso al artículo completo |