Colouring isonemal fabrics with more than two colours by thick striping

Authors

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

DOI:

https://doi.org/10.11575/cdm.v8i1.62180

Keywords:

weaving, isonemal fabric, striping, colouring

Abstract

Perfect colouring of isonemal fabrics by thin and thick striping of warp and weft with more than two colours is introduced. Conditions that prevent perfect colouring by striping are derived, and it is shown that avoiding them is sufficient to allow it. Examples of thick striping in all possible species are given.

Author Biography

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

retired rull professor

Dept of Mathematics

References

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J.A.~Hoskins and R.S.D.~Thomas [1991]: `The patterns of the isonemal two-colour two-way two-fold fabrics', {\em Bull.~Austral.~Math.~Soc.} {\bf 44}, 33--43.

Richard L.~Roth [1993]: `The symmetry groups of periodic isonemal fabrics', {\em Geometriae Dedicata} {\bf 48}, 191--210.

------ [1995]: `Perfect colorings of isonemal fabrics using two colors', {\em Geometriae Dedicata} {\bf 56}, 307--326.

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R.S.D.~Thomas [2009]: `Isonemal Prefabrics with Only Parallel Axes of Symmetry', {\em Discrete Mathematics} {\bf 309}, 2696--2711.

------ [2010a]: `Isonemal Prefabrics with Perpendicular Axes of Symmetry', {\em Utilitas Mathematica} {\bf 82}, 33--70.

------ [2010b]: `Isonemal Prefabrics with no Axes of Symmetry', {\em Discrete Mathematics} {\bf 310}, 1307--1324.

------ [2011]: `Perfect colourings of isonemal fabrics by thin striping', {\em Bull.~Australian Math.~Soc.} {\bf 83}, 63--86.

------ [2012]: `Perfect colourings of isonemal fabrics by thick striping', {\em Bull.~Australian Math.~Soc.} {\bf 85}, 325--349.

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Published

2013-07-29

Issue

Vol. 8 No. 1 (2013)

Section

Articles

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