Interesting Esoterica

Zeroless Arithmetic: Representing Integers ONLY using ONE

Article by Ghang, EK and Zeilberger, Doron
  • Published in 2013
  • Added on
We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the inputs are ones. We also describe efficient algorithms for the random generation of such representations, and use Dynamical Programming to find a shortest possible formula representing any given positive integer.

Links

Other information

key
Ghang2013
type
article
date_added
2013-03-07
date_published
2013-03-01
arxivId
1303.0885
isbn
1111111111
journal
arXiv preprint arXiv:1303.0885
pages
1--7

BibTeX entry

@article{Ghang2013,
	key = {Ghang2013},
	type = {article},
	title = {Zeroless Arithmetic: Representing Integers ONLY using ONE},
	author = {Ghang, EK and Zeilberger, Doron},
	abstract = {We use recurrence equations (alias difference equations) to enumerate the number of formula-representations of positive integers using only addition and multiplication, and using addition, multiplication, and exponentiation, where all the inputs are ones. We also describe efficient algorithms for the random generation of such representations, and use Dynamical Programming to find a shortest possible formula representing any given positive integer.},
	comment = {},
	date_added = {2013-03-07},
	date_published = {2013-03-01},
	urls = {http://arxiv.org/abs/1303.0885,http://arxiv.org/pdf/1303.0885v2},
	collections = {Unusual arithmetic,Easily explained,Integerology},
	archivePrefix = {arXiv},
	arxivId = {1303.0885},
	eprint = {1303.0885},
	isbn = 1111111111,
	journal = {arXiv preprint arXiv:1303.0885},
	month = {mar},
	pages = {1--7},
	url = {http://arxiv.org/abs/1303.0885 http://arxiv.org/pdf/1303.0885v2},
	year = 2013,
	primaryClass = {math.CO},
	urldate = {2013-03-07}
}