en>Yobot: /* Example of dynamic logic operations */WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

2013-03-07T16:43:41Z

Example of dynamic logic operations: WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

← Older revision		Revision as of 18:43, 7 March 2013
Line 1:		Line 1:
	~~My name~~ is [http://~~Www~~.~~Google~~.de/~~search?q~~=~~kendall&prmd~~=~~ivnsb&source~~=~~univ&tbm~~=~~nws&tbo~~=~~u&sa~~=~~X&ei~~=~~jd5FVL~~-~~fApWPNrXNgLgO&ved~~=~~0CCYQqAI Kendall] (45 years old) and my hobbies are Herpetoculture and Volleyball~~.~~<br><br>Here is my webpage~~ - ~~[https~~://www.~~youtube~~.~~com~~/~~user~~/~~MineCraftGTAgameplay GTA~~]		In [[combinatorics]], '''Sun's curious identity''' is the following [[Identity (mathematics)\|identity]] involving [[binomial coefficient]]s, first established by [[Zhi-Wei Sun]] in 2002:

			:<math>
			(x+m+1)\sum_{i=0}^m(-1)^i\dbinom{x+y+i}{m-i}\dbinom{y+2i}{i}
			-\sum_{i=0}^{m}\dbinom{x+i}{m-i}(-4)^i=(x-m)\dbinom{x}{m}.
			</math>

			After Sun's publication of this identity, five other proofs were obtained by various mathematicians: they are Panholzer and Prodinger's proof via [[generating functions]], Merlini and Sprugnoli's proof using [[Riordan arrays]], Ekhad and Mohammed's proof by the [[WZ theory\|WZ]] method, Chu and Claudio's proof with the help of [[Johan Jensen (mathematician)\|Jensen]]'s formula, and Callan's [[combinatorial proof]] involving [[dominos]] and colorings.

			An application of the identity was given by Sun in a recent paper.

			==References==

			*{{citation
			\| last = Callan \| first = D.
			\| arxiv = math.CO/0401216
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A05
			\| title = A combinatorial proof of Sun's 'curious' identity
			\| url = http://www.emis.de/journals/INTEGERS/papers/e5/e5.pdf
			\| volume = 4
			\| year = 2004}}.

			*{{citation
			\| last1 = Chu \| first1 = W.
			\| last2 = Claudio \| first2 = L.V.D.
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A20
			\| title = Jensen proof of a curious binomial identity
			\| url = http://www.emis.de/journals/INTEGERS/papers/d20/d20.pdf
			\| volume = 3
			\| year = 2003}}.

			*{{citation
			\| last1 = Ekhad \| first1 = S. B. \| author1-link = Doron Zeilberger
			\| last2 = Mohammed \| first2 = M.
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A06
			\| title = A WZ proof of a 'curious' identity
			\| url = http://www.emis.de/journals/INTEGERS/papers/d6/d6.pdf
			\| volume = 3
			\| year = 2003}}.

			*{{citation
			\| last1 = Merlini \| first1 = D.
			\| last2 = Sprugnoli \| first2 = R.
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A08
			\| title = A Riordan array proof of a curious identity
			\| url = http://www.emis.de/journals/INTEGERS/papers/c8/c8.pdf
			\| volume = 2
			\| year = 2002}}.

			*{{citation
			\| last1 = Panholzer \| first1 = A.
			\| last2 = Prodinger \| first2 = H.
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A06
			\| title = A generating functions proof of a curious identity
			\| url = http://www.emis.de/journals/INTEGERS/papers/c6/c6.pdf
			\| volume = 2
			\| year = 2002}}.

			*{{citation
			\| last = Sun \| first = Zhi-Wei
			\| journal = Integers: Electronic Journal of Combinatorial Number Theory
			\| page = A04
			\| title = A curious identity involving binomial coefficients
			\| url = http://www.emis.de/journals/INTEGERS/papers/c4/c4.pdf
			\| volume = 2
			\| year = 2002}}.

			*{{citation
			\| last = Sun \| first = Zhi-Wei
			\| doi = 10.1016/j.disc.2007.08.046
			\| arxiv = math.NT/0404385
			\| issue = 18
			\| journal = [[Discrete Mathematics (journal)\|Discrete Mathematics]]
			\| pages = 4231–4245
			\| title = On sums of binomial coefficients and their applications
			\| volume = 308
			\| year = 2008}}.

			[[Category:Factorial and binomial topics]]
			[[Category:Mathematical identities]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-08T20:04:59Z

ISBNs (Build KE)

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My name is [http://Www.Google.de/search?q=kendall&prmd=ivnsb&source=univ&tbm=nws&tbo=u&sa=X&ei=jd5FVL-fApWPNrXNgLgO&ved=0CCYQqAI Kendall] (45 years old) and my hobbies are Herpetoculture and Volleyball.<br><br>Here is my webpage - [https://www.youtube.com/user/MineCraftGTAgameplay GTA]

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en>Yobot: /* Example of dynamic logic operations */WP:CHECKWIKI errors fixed + general fixes using AWB (8961)

en>Helpful Pixie Bot: ISBNs (Build KE)