Zeroless Arithmetic: Representing Integers ONLY using ONE

• Published in 2013
• Added on 2013-03-07

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

• http://arxiv.org/abs/1303.0885
• http://arxiv.org/pdf/1303.0885v2

Other information

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}
}