Sequence knitting

Abstract

Sequence knitting comes from a straightforward directive; determine a short basic sequence of stitches and create a piece by continuous repetition of that sequence. This paper determines the number of sequence knitting patterns. We restrict our attention to sequences containing only knit and purl stitches and to flat knitting. We further assume that a sequence is restarted at the beginning of each row of knitting, but we do not assume that the number of stitches cast on is a multiple of the sequence length. We consider the case that a pattern and its left/right mirror image are the same, and the case that a pattern and its left/right mirror image are not necessarily the same.

GRAPHICAL ABSTRACT

Keywords:

• Sequence knitting
• necklaces
• bracelets
• symmetry
• antisymmetry
• chirality
• orbits
• group action
• combinatorics
• abstract algebra

Acknowledgments

The author wishes to thank the reviewers for their helpful suggestions, especially Carolyn Yackel and sarah-marie belcastro. The author would also like to thank Janet Goodman for inspiring the work.

Disclosure statement

No potential conflict of interest was reported by the author(s).