TY - JOUR

T1 - Moduli Space of a Planar Polygonal Linkage: A Combinatorial Description

AU - Панина, Гаянэ Юрьевна

PY - 2017

Y1 - 2017

N2 - We describe and study an explicit structure of a regular cell complex K(L)K(L) on the moduli space M(L) of a planar polygonal linkage L. The combinatorics is very much related (but not equal) to the combinatorics of the permutohedron. In particular, the cells of maximal dimension are labeled by elements of the symmetric group. For example, if the moduli space M is a sphere, the complex KK is dual to the boundary complex of the permutohedron.The dual complex K∗K∗ is patched of Cartesian products of permutohedra. It can be explicitly realized in the Euclidean space via a surgery on the permutohedron.

AB - We describe and study an explicit structure of a regular cell complex K(L)K(L) on the moduli space M(L) of a planar polygonal linkage L. The combinatorics is very much related (but not equal) to the combinatorics of the permutohedron. In particular, the cells of maximal dimension are labeled by elements of the symmetric group. For example, if the moduli space M is a sphere, the complex KK is dual to the boundary complex of the permutohedron.The dual complex K∗K∗ is patched of Cartesian products of permutohedra. It can be explicitly realized in the Euclidean space via a surgery on the permutohedron.

KW - Polygonal linkage Cell complex CW-complex Configuration space Moduli space Permutohedron Cyclic polytope

U2 - 10.1007/s40598-017-0070-1

DO - 10.1007/s40598-017-0070-1

M3 - Article

VL - 3

SP - 351

EP - 364

JO - Arnold Mathematical Journal

JF - Arnold Mathematical Journal

SN - 2199-6792

IS - 3

ER -