Colouring isonemal fabrics with more than two colours by thin striping

Authors

  • Robert Thomas St John's College and University of Manitoba

DOI:

https://doi.org/10.11575/cdm.v9i2.62210

Keywords:

colour, fabric, isonemal, striping, weaving

Abstract

Perfect colouring of isonemal fabrics by thin striping of warp and weft with more than two colours is examined. Examples of thin striping in all possible species with no redundancy and with redundant cells arranged as twills are given. Colouring woven flat tori is discussed.

 

Author Biography

Robert Thomas, St John's College and University of Manitoba

retired full professor

Dept of Mathematics

References

\bibitem[1]{Roth1993} Roth, Richard L., `The symmetry groups of periodic isonemal fabrics', \emph{Geometriae Dedicata} \textbf{48} (1993), 191--210.

\bibitem[2]{Roth1995} Roth, Richard L., `Perfect colorings of isonemal fabrics using two colors', \emph{Geometriae Dedicata} \textbf{56} (1995), 307--326.

\bibitem[3]{Thomas2009} Thomas, R.S.D., `Isonemal prefabrics with only parallel axes of sym\-metry', \emph{Discrete Mathematics} \textbf{309} (2009), 2696--2711. doi:10.1016/j.disc.2008.06.028. Online: \url{http://arxiv.org/abs/math/0612808v2} and on the journal site.

\bibitem[4]{Thomas2010a} Thomas, R.S.D., `Isonemal prefabrics with perpendicular axes of symmetry', \emph{Utilitas Mathematica} \textbf{82} (2010), 33--70. Online: \url{http://arxiv.org/abs/0805.3791v1}.

\bibitem[5]{Thomas2010b} Thomas, R.S.D., `Isonemal prefabrics with no axes of symmetry', \emph{Discrete Mathematics} \textbf{310} (2010), 1307--1324. doi:10.1016/j.disc.2009.12.015. Online: \url{http://arxiv.org/abs/0911.1467v2} and on the journal site.

\bibitem[6]{Thomas2011} Thomas, R.S.D., `Perfect colourings of isonemal fabrics by thin striping', \emph{Bull.~Australian Math.~Soc.} \textbf{83} (2011), 63--86.

Online: \url{http://arxiv.org/abs/1006.5653} and on the journal site, doi:10.1017/S0004972710001632.

\bibitem[7]{Thomas2012} Thomas, R.S.D., `Perfect colourings of isonemal fabrics by thick striping', \emph{Bull.~Australian Math.~Soc.} \textbf{85} (2012), 325--349.

Online: \url{http://arxiv.org/abs/1109.2254} and on the journal site, doi:10.1017/S0004972711002899.

\bibitem[8]{ThomasMS} Thomas, R.S.D., `Colouring isonemal fabrics with more than two colours by thick striping', \emph{Contributions to Discrete Mathematics}, to appear. Online: \url{http://arxiv.org/abs/1305.1061}.

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Published

2014-12-30

Issue

Vol. 9 No. 2 (2014)

Section

Articles

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