Paper by Erik D. Demaine

Reference:

Therese Biedl, Erik Demaine, Martin Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, and Sue Whitesides, “A Note on Reconfiguring Tree Linkages: Trees can Lock”, Discrete Applied Mathematics, volume 117, number 1–3, 2002, pages 293–297.

BibTeX

@Article{LockedTreeDAM,
  AUTHOR        = {Therese Biedl and Erik Demaine and Martin Demaine
                   and Sylvain Lazard and Anna Lubiw and Joseph O'Rourke
                   and Steve Robbins and Ileana Streinu and Godfried Toussaint
                   and Sue Whitesides},
  TITLE         = {A Note on Reconfiguring Tree Linkages: Trees can Lock},
  JOURNAL       = {Discrete Applied Mathematics},
  JOURNALURL    = {http://www.elsevier.com/locate/dam},
  VOLUME        = 117,
  NUMBER        = {1--3},
  YEAR          = 2002,
  PAGES         = {293--297},

  PAPERS        = {LockedTreeTR; CCCG98c},
  replaces      = {CCCG98c},
  LENGTH        = {5 pages},
  WEBPAGES      = {linkage},
  dblp          = {https://dblp.org/rec/journals/dam/BiedlDDLLORSTW02},
  comments      = {This paper is also available from <A HREF="https://doi.org/10.1016/S0166-218X(01)00229-3">ScienceDirect</A>.},
}

Abstract:

It has recently been shown that any polygonal chain in the plane can be reconfigured to lie on a straight line, and any polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two configurations that are not connected by a motion. Indeed, we prove that an N-link tree can have 2^Ω(N) equivalence classes of configurations.

Comments:

This paper is also available from ScienceDirect.

Length:

The paper is 5 pages.

Availability:

The paper is available in PostScript (360k) and gzipped PostScript (68k).

See information on file formats.

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Related papers:

LockedTreeTR (On Reconfiguring Tree Linkages: Trees can Lock)

CCCG98c (On Reconfiguring Tree Linkages: Trees can Lock)

Related webpages:

Carpenter's Rule Theorem