More ties than we thought

• Published in 2014
• Added on 2014-02-06

We extend the existing enumeration of neck tie knots to include tie knots with a textured front, tied with the narrow end of a tie. These tie knots have gained popularity in recent years, based on reconstructions of a costume detail from The Matrix Reloaded, and are explicitly ruled out in the enumeration by Fink and Mao (2000). We show that the relaxed tie knot description language that comprehensively describes these extended tie knot classes is either context sensitive or context free. It has a sub-language that covers all the knots that inspired the work, and that is regular. From this regular sub-language we enumerate 177 147 distinct tie knots that seem tieable with a normal necktie. These are found through an enumeration of 2 046 winding patterns that can be varied by tucking the tie under itself at various points along the winding.

Links

• http://arxiv.org/abs/1401.8242
• http://arxiv.org/pdf/1401.8242v2

Other information

BibTeX entry

@article{Hirsch2014,
	key = {Hirsch2014},
	type = {article},
	title = {More ties than we thought},
	author = {Hirsch, Dan and Patterson, Meredith L and Sandberg, Anders and Vejdemo-Johansson, Mikael},
	abstract = {We extend the existing enumeration of neck tie knots to include tie knots with a textured front, tied with the narrow end of a tie. These tie knots have gained popularity in recent years, based on reconstructions of a costume detail from The Matrix Reloaded, and are explicitly ruled out in the enumeration by Fink and Mao (2000).   We show that the relaxed tie knot description language that comprehensively describes these extended tie knot classes is either context sensitive or context free. It has a sub-language that covers all the knots that inspired the work, and that is regular. From this regular sub-language we enumerate 177 147 distinct tie knots that seem tieable with a normal necktie. These are found through an enumeration of 2 046 winding patterns that can be varied by tucking the tie under itself at various points along the winding.},
	comment = {},
	date_added = {2014-02-06},
	date_published = {2014-01-01},
	urls = {http://arxiv.org/abs/1401.8242,http://arxiv.org/pdf/1401.8242v2},
	collections = {Attention-grabbing titles,Easily explained},
	month = {jan},
	url = {http://arxiv.org/abs/1401.8242 http://arxiv.org/pdf/1401.8242v2},
	year = 2014,
	archivePrefix = {arXiv},
	eprint = {1401.8242},
	primaryClass = {cs.FL},
	urldate = {2014-02-06}
}