en>Nick Number: repaired link(s) to disambiguation pages (you can help) - Monomorphic

2013-12-27T20:58:36Z

repaired link(s) to disambiguation pages (you can help) - Monomorphic

← Older revision		Revision as of 22:58, 27 December 2013
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	~~Hello~~. ~~Allow me introduce~~ the ~~author~~. ~~Her~~ title is ~~Emilia Shroyer but~~ it's ~~not~~ the ~~most feminine title out there~~. ~~I am a meter reader~~. ~~California is our beginning location~~. ~~Body developing is what my family members~~ and ~~I appreciate~~.<br><br>~~Here is my webpage~~ - [http://~~www~~.~~videokeren~~.~~com~~/~~user~~/~~BFlockhar over the counter std test~~]		In [[number theory]], '''zero-sum problems''' are a certain class of [[combinatorial]] questions. In general, a [[finite abelian group]] ''G'' is considered. The zero-sum problem for the integer ''n'' is the following: Find the smallest integer ''k'' such that every sequence of elements of ''G'' with length <math>k</math> contains ''n'' terms that sum to [[identity element\|0]].

			In 1961 [[Paul Erdős]], [[Abraham Ginzburg]], and [[Abraham Ziv]] proved the general result for <math>\mathbb{Z}/n\mathbb{Z}</math> (the integers [[modular arithmetic\|mod]] n) that<ref>{{cite journal \| zbl=0063.00009 \| last1=Erdős \| first1=Paul \| last2=Ginzburg \| first2=A. \| last3=Ziv \| first3=A. \| title=A theorem in additive number theory \| journal=Bull. Res. Council Israel \| volume=10F \| pages=41–43 \| year=1961 }}</ref>

			:<math>k = 2n - 1.\ </math>

			Explicitly this says that any [[multiset]] of 2''n'' − 1 integers has a subset of size ''n'' the sum of whose elements is a multiple of ''n''. This result is known as the '''Erdős–Ginzburg–Ziv theorem''' after its discoverers: it may be deduced from the [[Cauchy-Davenport theorem]].<ref name=N48>Nathanson (1996) p.48</ref>

			More general results than this theorem exist, such as [[Olson's theorem]], [[Kemnitz's conjecture]] (proved by [[Christian Reiher]] in 2003<ref>{{Citation \|last=Reiher \|first=Christian \|title=On Kemnitz' conjecture concerning lattice-points in the plane \|journal=The Ramanujan Journal \|volume=13 \|issue=1–3 \|year=2007 \|doi=10.1007/s11139-006-0256-y \|pages=333–337 \| zbl=1126.11011 }}.</ref>), and the [[weighted EGZ theorem]] (proved by [[David J. Grynkiewicz]] in 2005<ref>{{Citation \|last=Grynkiewicz \|first=D. J. \|title=A Weighted Erdős-Ginzburg-Ziv Theorem \|journal=Combinatorica \|volume=26 \|issue=4 \|pages=445–453 \|year=2006 \|doi=10.1007/s00493-006-0025-y \| zbl=1121.11018 }}.</ref>).

			==See also==
			* [[Davenport constant]]
			* [[Subset sum problem]]

			==References==
			{{Reflist}}
			* {{cite book \| last=Geroldinger \| first=Alfred \| chapter=Additive group theory and non-unique factorizations \| pages=1-86 \| editor1-last=Geroldinger \| editor1-first=Alfred \| editor2-last=Ruzsa \| editor2-first=Imre Z. \| others=Elsholtz, C.; Freiman, G.; Hamidoune, Y. O.; Hegyvári, N.; Károlyi, G.; Nathanson, M.; Solymosi, J.; Stanchescu, Y. With a foreword by Javier Cilleruelo, Marc Noy and Oriol Serra (Coordinators of the DocCourse) \| title=Combinatorial number theory and additive group theory \| series=Advanced Courses in Mathematics CRM Barcelona \| location=Basel \| publisher=Birkhäuser \| year=2009 \| isbn=978-3-7643-8961-1 \| zbl=1221.20045 }}
			* {{cite book \| first=Melvyn B. \| last=Nathanson \| title=Additive Number Theory: Inverse Problems and the Geometry of Sumsets \| volume=165 \| series=[[Graduate Texts in Mathematics]] \| publisher=[[Springer-Verlag]] \| year=1996 \| isbn=0-387-94655-1 \| zbl=0859.11003 }}

			==External links==
			* {{springer\|title=Erdős-Ginzburg-Ziv theorem\|id=p/e110100}}
			* PlanetMath [http://planetmath.org/encyclopedia/ErdHosGinzburgZivTheorem.html Erdős, Ginzburg, Ziv Theorem]
			* [[Zhi-Wei Sun\|Sun, Zhi-Wei]], [http://math.nju.edu.cn/~zwsun/csz.htm "Covering Systems, Restricted Sumsets, Zero-sum Problems and their Unification"]

			[[Category:Combinatorics]]
			[[Category:Paul Erdős]]
			[[Category:Mathematical problems]]

en>Mathiastck at 17:29, 4 June 2009

2009-06-04T17:29:04Z

New page

Hello. Allow me introduce the author. Her title is Emilia Shroyer but it's not the most feminine title out there. I am a meter reader. California is our beginning location. Body developing is what my family members and I appreciate.<br><br>Here is my webpage - [http://www.videokeren.com/user/BFlockhar over the counter std test]

Evolutionarily stable state - Revision history

en>Nick Number: repaired link(s) to disambiguation pages (you can help) - Monomorphic

en>Mathiastck at 17:29, 4 June 2009