Research output: Contribution to journal › Article › peer-review
Cyclopermutohedron. / Panina, G.Y.
In: Proceedings of the Steklov Institute of Mathematics, No. 1, 2015, p. 132-144.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Cyclopermutohedron
AU - Panina, G.Y.
PY - 2015
Y1 - 2015
N2 - © 2015, Pleiades Publishing, Ltd.It is well known that the k-faces of the permutohedron Πn can be labeled by (all possible) linearly ordered partitions of the set [n] = {1,.., n} into n − k nonempty parts. The incidence relation corresponds to the refinement: a face F contains a face F′ whenever the label of F′ refines the label of F. We consider the cell complex CPn+1 defined in a similar way but with the linear ordering replaced by the cyclic ordering. Namely, the k-cells of the complex CPn+1 are labeled by (all possible) cyclically ordered partitions of the set [n + 1] = {1,.., n + 1} into n + 1 − k > 2 nonempty parts. The incidence relation in CPn+1 again corresponds to the refinement: a cell F contains a cell F′ whenever the label of F′ refines the label of F. The complex CPn+1 cannot be represented by a convex polytope, since it is not a combinatorial sphere (not even a combinatorial manifold). However, it can be represented by some virtual polytope
AB - © 2015, Pleiades Publishing, Ltd.It is well known that the k-faces of the permutohedron Πn can be labeled by (all possible) linearly ordered partitions of the set [n] = {1,.., n} into n − k nonempty parts. The incidence relation corresponds to the refinement: a face F contains a face F′ whenever the label of F′ refines the label of F. We consider the cell complex CPn+1 defined in a similar way but with the linear ordering replaced by the cyclic ordering. Namely, the k-cells of the complex CPn+1 are labeled by (all possible) cyclically ordered partitions of the set [n + 1] = {1,.., n + 1} into n + 1 − k > 2 nonempty parts. The incidence relation in CPn+1 again corresponds to the refinement: a cell F contains a cell F′ whenever the label of F′ refines the label of F. The complex CPn+1 cannot be represented by a convex polytope, since it is not a combinatorial sphere (not even a combinatorial manifold). However, it can be represented by some virtual polytope
U2 - 10.1134/S0081543815010101
DO - 10.1134/S0081543815010101
M3 - Article
SP - 132
EP - 144
JO - Proceedings of the Steklov Institute of Mathematics
JF - Proceedings of the Steklov Institute of Mathematics
SN - 0081-5438
IS - 1
ER -
ID: 4012406