2017
DOI: 10.1007/s40598-017-0070-1
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Moduli Space of a Planar Polygonal Linkage: A Combinatorial Description

Abstract: Abstract. We describe and study an explicit structure of a regular cell complex 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 K is dual to the boundary complex of the permutohedron.The dual complex K * is patched of Cartesian products of permuto… Show more

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Cited by 14 publications
(20 citation statements)
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“…• As it was shown in [8], M (L) admits a structure of a regular cell complex. The combinatorics is very much related (but not equal) to the combinatorics of the permutahedron.…”
Section: Introductionmentioning
confidence: 88%
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“…• As it was shown in [8], M (L) admits a structure of a regular cell complex. The combinatorics is very much related (but not equal) to the combinatorics of the permutahedron.…”
Section: Introductionmentioning
confidence: 88%
“…In Section 3 we associate with a quasilinkage Q a cell complex CW M (Q) by applying the rules from [8]. We prove that CW M (Q) is locally isomorphic to CW M (L) for some real linkage L (however, L depends on the location, and there may be no real linkage associated to the entire complex).…”
Section: Remarkmentioning
confidence: 99%
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