A mathematician knits an afghan and counts the number of possible patterns

Abstract

The Hue Shift afghan consists of 100 squares knit with 10 colours in a manner determined by a diagram. How many ways can you knit a Hue Shift afghan? What makes an afghan a Hue Shift is defined. Then the number of different afghans is determined up to symmetry considering colour order, stripe order, and direction of knitting for each square.

GRAPHICAL ABSTRACT

Keywords:

• Knitting
• combinatorics
• afghan
• algebra
• recreational math

Acknowledgments

Thank you to Knitpicks for welcoming me to write about their pattern. Thank you to Carolyn Yackel and Sarah-Marie Belcastro for encouraging me to write this paper. Thank you to Hannah Bellwoar, Belle Tuten, Carolyn Yackel, Kristin Camenga, Sarah-Marie Belcastro, and the reviewers for reading and commenting on drafts of this paper.

Disclosure statement

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