Finding and counting MSTD sets

Geoffrey Iyer; Oleg Lazarev; Steven J. Miller; Liyang Zhang

doi:10.1007/978-1-4939-1601-6_7

Finding and counting MSTD sets

Geoffrey Iyer
, Oleg Lazarev
, Steven J. Miller
, Liyang Zhang

Mathematics

University of Michigan, Ann Arbor
Princeton University
Williams College

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We review the basic theory of more sums than differences (MSTD) sets, specifically their existence, simple constructions of infinite families, the proof that a positive percentage of sets under the uniform binomial model are MSTD but not if the probability that each element is chosen tends to zero, and “explicit” constructions of large families of MSTD sets. We conclude with some new constructions and results of generalized MSTD sets, including among other items results on a positive percentage of sets having a given linear combination greater than another linear combination, and a proof that a positive percentage of sets are k-generational sum-dominant (meaning A, A C A,...., kA D A+... +A are each sum-dominant).

Original language	English
Title of host publication	Combinatorial and Additive Number Theory - CANT 2011 and 2012
Editors	Melvyn B. Nathanson
Publisher	Springer New York LLC
Pages	79-98
Number of pages	20
ISBN (Electronic)	9781493916009
DOIs	https://doi.org/10.1007/978-1-4939-1601-6_7
State	Published - 2014
Event	School on Combinatorics, Automata and Number Theory, CANT 2012 - Marseille, France Duration: May 21 2012 → May 25 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	101
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	School on Combinatorics, Automata and Number Theory, CANT 2012
Country/Territory	France
City	Marseille
Period	5/21/12 → 5/25/12

ASJC Scopus Subject Areas

General Mathematics

Keywords

More sum than difference sets

Access to Document

10.1007/978-1-4939-1601-6_7

Cite this

Finding and counting MSTD sets. / Iyer, Geoffrey; Lazarev, Oleg; Miller, Steven J. et al.
Combinatorial and Additive Number Theory - CANT 2011 and 2012. ed. / Melvyn B. Nathanson. Springer New York LLC, 2014. p. 79-98 (Springer Proceedings in Mathematics and Statistics; Vol. 101).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Iyer, G, Lazarev, O, Miller, SJ & Zhang, L 2014, Finding and counting MSTD sets. in MB Nathanson (ed.), Combinatorial and Additive Number Theory - CANT 2011 and 2012. Springer Proceedings in Mathematics and Statistics, vol. 101, Springer New York LLC, pp. 79-98, School on Combinatorics, Automata and Number Theory, CANT 2012, Marseille, France, 5/21/12. https://doi.org/10.1007/978-1-4939-1601-6_7

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AB - We review the basic theory of more sums than differences (MSTD) sets, specifically their existence, simple constructions of infinite families, the proof that a positive percentage of sets under the uniform binomial model are MSTD but not if the probability that each element is chosen tends to zero, and “explicit” constructions of large families of MSTD sets. We conclude with some new constructions and results of generalized MSTD sets, including among other items results on a positive percentage of sets having a given linear combination greater than another linear combination, and a proof that a positive percentage of sets are k-generational sum-dominant (meaning A, A C A,...., kA D A+... +A are each sum-dominant).

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Finding and counting MSTD sets

Abstract

Publication series

Conference

ASJC Scopus Subject Areas

Keywords

Access to Document

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