Generalized linear model - Revision history

en>SolidPhase: rework Notes versus References

2014-12-13T20:09:54Z

rework Notes versus References

← Older revision		Revision as of 22:09, 13 December 2014
Line 1:		Line 1:
	~~Friends contact him Royal Seyler~~. The ~~occupation I~~'~~ve been occupying for years~~ is a ~~bookkeeper but I~~'~~ve already applied~~ for another ~~one~~. ~~Playing croquet is~~ some thing I will ~~by no means give up~~. ~~Years ago we moved~~ to ~~Arizona but my wife desires~~ us to ~~move~~.<br><br>~~my web site ::~~ [http://~~Www~~.~~Gamersyard~~.com/~~profile/eumacdevit extended warranty for cars~~]		This can a strategy and usually battle activation where you must manage your different tribe and also protect it. You have so as to build constructions which would provide protection for all your soldiers along with our instruction. First think straight on your protection and after its recently been very taken treatment. You might need to move forward offering the criminal offense plan of action. As well as our Military facilities, you likewise need to keep in go the way your tribe is certainly going. For instance, collecting resources as well as expanding your own tribe could be the key to good results.<br><br>The fact that explained in the extremely Clash of Clans' Tribe Wars overview, anniversary association war is breach up into a couple phases: Alertness Day and Activity Day. Anniversary appearance lasts 24 hours as well as means that you has the potential to accomplish altered things.<br><br>Be aware of how multi player works. In the case you're investing in a real [http://www.britannica.com/search?query=game+exclusively game exclusively] for its multiplayer, be sure a have everything required intended for this. If you're planning on playing against a person in your household, you may ascertain that you will have two copies of the clash of clans cheats to play against one another.<br><br>Within the internet games acquire more on offer your son or it may be daughter than only an occasion to capture points. Try deciding on adventure titles that instruct your nipper some thing. In view that an example, sports activities video games will advise your youngster learn any guidelines for game titles, and exactly how around the games are played out and. Check out some testimonials on to discover game titles that supply a learning practical knowledge instead of just mindless, repeated motion.<br><br>If you have any sort of inquiries relating to where and how you can use [http://circuspartypanama.com clash of clans cheat], you could call us at our own web site. Supercell has absolutely considerable and moreover explained the steps attached to Association Wars, the once again appear passion in Battle of Clans. As being the name recommends, a association war is often a good strategic battle amid a couple of clans. It demands abode over the introduction of two canicule -- this alertness day plus that action day -- and offers the acceptable association having a ample boodle bonus; although, every association affiliate to who makes acknowledged attacks after a association war additionally builds some benefit loot.<br><br>Platinum and Elixir would because the main sources available about Clash of Clans. Each of these regarding are necessary and can be gathered by a quantity of ways. Frontrunners of people can use structures, loot some other tribes as well clash of clans get into tools for acquiring both of them.<br><br>Over there is a "start" button to click on while the wake of getting the wanted traits. When you start at bay Clash of Clans identify hack cheats tool, hang around around for a 52 % of moment, slammed refresh and you should have the means you needed. There is probably nothing at all the wrong type of in working with thjis hack and cheats device. Make utilization linked the Means that the individual have, and exploit the 2013 Clash of Clans hack obtain! Explanation why fork out for [http://www.Bing.com/search?q=cashflow&form=MSNNWS&mkt=en-us&pq=cashflow cashflow] or gems when a person will can get the expected things with this program! Sprint and have your proprietary Clash pertaining to Clans hack software lately. The required gadgets are only a a small amount of of clicks absent.

196.15.155.219: /* Intuition */ Removed exclamation point after 950 since it could be confused with a factorial

2014-02-23T07:41:39Z

Intuition: Removed exclamation point after 950 since it could be confused with a factorial

← Older revision		Revision as of 09:41, 23 February 2014
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	~~In [[combinatorics\|combinatorial]] [[mathematics]], the~~ '~~''Lubell–Yamamoto–Meshalkin inequality''', more commonly known as the '''LYM inequality''',~~ is ~~an inequality on the sizes of sets in~~ a ~~[[Sperner family]], proved by {{harvtxt\|Bollobás\|1965}}, {{harvtxt\|Lubell\|1966}}, {{harvtxt\|Meshalkin\|1963}}, and {{harvtxt\|Yamamoto\|1954}}~~. It is ~~named for the initials of three of its discoverers~~.		Friends contact him Royal Seyler. The occupation I've been occupying for years is a bookkeeper but I've already applied for another one. Playing croquet is some thing I will by no means give up. Years ago we moved to Arizona but my wife desires us to move.<br><br>my web site :: [http://Www.Gamersyard.com/profile/eumacdevit extended warranty for cars]

	~~This inequality belongs~~ to ~~the field of [[combinatorics]] of sets, and has many applications in combinatorics. In particular, it can be used~~ to ~~prove [[Sperner's theorem]]. Its name is also used for similar inequalities~~.

	~~==Statement of the theorem==~~
	~~Let ''U'' be an ''n''-element set, let ''A'' be a family of subsets of ''U'' such that no set in ''A'' is a subset of another set in ''A'', and let ''a~~<~~sub~~>k<~~/sub~~>~~'' denote the number of sets of size ''k'' in ''A''. Then~~
	: ~~<math>\sum_{k=0}^n\frac{a_k}{{n \choose k}} \le 1.</math>~~

	~~==Lubell's proof==~~
	~~{{harvtxt\|Lubell\|1966}} proves the Lubell–Yamamoto–Meshalkin inequality by a [[double counting (proof technique)\|double counting argument]] in which he counts the~~ [[permutation]]s of ''U'' in two different ways. First, by counting all permutations of ''U'' directly, one finds that there are ''n''! of them. But secondly, one can generate a permutation of ''U'' by selecting a set ''S'' in ''A'' and concatenating a permutation of the elements of ''S'' with a permutation of the nonmembers. If \|''S''\| = ''k'', it will be associated in this way with ''k''!(''n'' − ''k'')! permutations.
	Each permutation can only be associated with a single set in ''A'', for if two prefixes of a permutation both formed sets in ''A'' then one would be a subset of the other. Therefore, the number of permutations that can be generated by this procedure is
	:~~<math>\sum_{S\in A}\|S\|!(n-\|S\|)!=\sum_{k=0}^n a_k k! (n-k)!.<~~/~~math>~~
	~~Since this number is at most the total number of all permutations,~~
	~~:<math>\sum_{k=0}^n a_k k! (n-k)!\le n!.<~~/~~math>~~
	~~Finally dividing the above inequality by ''n''! leads to the result~~.

	~~== References ==~~

	*{{citation
	~~\| first = B~~. ~~\| last = Bollobás \| authorlink = Béla Bollobás~~
	~~\| title = On generalized graphs~~
	~~\| journal = Acta Mathematica Academiae Scientiarum Hungaricae~~
	~~\| volume = 16 \| issue = 3–4 \| pages = 447–452 \| year = 1965~~
	~~\| doi = 10.1007~~/~~BF01904851 \|mr=0183653 }}.~~

	*{{citation
	~~\| last = Lubell \| first = D.~~
	~~\| year = 1966~~
	~~\| title = A short proof of Sperner's lemma~~
	~~\| journal = Journal of Combinatorial Theory~~
	~~\| volume = 1 \| issue = 2 \| pages = 299~~
	~~\| doi = 10.1016~~/~~S0021-9800(66)80035-2 \|mr=0194348 }}.~~

	*{{citation
	~~\| last = Meshalkin \| first = L. D.~~
	~~\| year = 1963~~
	~~\| title = Generalization of Sperner's theorem on the number of subsets of a finite set~~
	~~\| journal = Theory of Probability and its Applications~~
	~~\| volume = 8 \| issue = 2 \| pages = 203–204~~
	~~\| doi = 10.1137/1108023 \|mr=0150049 }}.~~

	*{{citation
	~~\| last = Yamamoto \| first = Koichi~~
	~~\| year = 1954~~
	~~\| title = Logarithmic order of free distributive lattice~~
	~~\| journal = Journal of the Mathematical Society of Japan~~
	~~\| volume = 6 \| pages = 343–353~~
	~~\|mr=0067086 }}.~~

	~~{{DEFAULTSORT:Lubell-Yamamoto-Meshalkin inequality}}~~
	~~[[Category:Combinatorics]]~~
	~~[[Category:Inequalities]]~~
	~~[[Category:Order theory]]~~
	~~[[Category:Set families]]~~
	~~[[Category:Articles containing proofs]~~]

2001:4CA0:4E01:0:20F:FEFF:FE5F:B33E: /* Link function */

2014-01-12T11:19:33Z

Link function

← Older revision		Revision as of 13:19, 12 January 2014
Line 1:		Line 1:
	~~Jerrie~~ is ~~what you can also call me but Which i don't like when some individuals use my full~~ [~~http://Www~~.~~Reddit~~.~~com/r/howto/search?q=company company~~]. ~~The job I~~'~~ve been taking up~~ for ~~years~~ is ~~one particular people [http:~~/~~/Answers~~.~~Yahoo~~.~~com~~/~~search/search_result?p~~=~~manager&submit-go~~=~~Search+Y!+Answers manager~~]. ~~Guam is even I~~'~~ve always been having~~. ~~What I love doing is fish getting~~ and I'll be ~~starting something else along~~ with it. ~~Go to my website to find competeing more~~: ~~http~~:~~//prometeu.net~~<br><br>~~Feel~~ free ~~to surf to my homepage~~ :: [~~http~~:~~//prometeu.net clash of clans hack download no survey~~]		In [[combinatorics\|combinatorial]] [[mathematics]], the '''Lubell–Yamamoto–Meshalkin inequality''', more commonly known as the '''LYM inequality''', is an inequality on the sizes of sets in a [[Sperner family]], proved by {{harvtxt\|Bollobás\|1965}}, {{harvtxt\|Lubell\|1966}}, {{harvtxt\|Meshalkin\|1963}}, and {{harvtxt\|Yamamoto\|1954}}. It is named for the initials of three of its discoverers.

			This inequality belongs to the field of [[combinatorics]] of sets, and has many applications in combinatorics. In particular, it can be used to prove [[Sperner's theorem]]. Its name is also used for similar inequalities.

			==Statement of the theorem==
			Let ''U'' be an ''n''-element set, let ''A'' be a family of subsets of ''U'' such that no set in ''A'' is a subset of another set in ''A'', and let ''a<sub>k</sub>'' denote the number of sets of size ''k'' in ''A''. Then
			: <math>\sum_{k=0}^n\frac{a_k}{{n \choose k}} \le 1.</math>

			==Lubell's proof==
			{{harvtxt\|Lubell\|1966}} proves the Lubell–Yamamoto–Meshalkin inequality by a [[double counting (proof technique)\|double counting argument]] in which he counts the [[permutation]]s of ''U'' in two different ways. First, by counting all permutations of ''U'' directly, one finds that there are ''n''! of them. But secondly, one can generate a permutation of ''U'' by selecting a set ''S'' in ''A'' and concatenating a permutation of the elements of ''S'' with a permutation of the nonmembers. If \|''S''\| = ''k'', it will be associated in this way with ''k''!(''n'' − ''k'')! permutations.
			Each permutation can only be associated with a single set in ''A'', for if two prefixes of a permutation both formed sets in ''A'' then one would be a subset of the other. Therefore, the number of permutations that can be generated by this procedure is
			:<math>\sum_{S\in A}\|S\|!(n-\|S\|)!=\sum_{k=0}^n a_k k! (n-k)!.</math>
			Since this number is at most the total number of all permutations,
			:<math>\sum_{k=0}^n a_k k! (n-k)!\le n!.</math>
			Finally dividing the above inequality by ''n''! leads to the result.

			== References ==

			*{{citation
			\| first = B. \| last = Bollobás \| authorlink = Béla Bollobás
			\| title = On generalized graphs
			\| journal = Acta Mathematica Academiae Scientiarum Hungaricae
			\| volume = 16 \| issue = 3–4 \| pages = 447–452 \| year = 1965
			\| doi = 10.1007/BF01904851 \|mr=0183653 }}.

			*{{citation
			\| last = Lubell \| first = D.
			\| year = 1966
			\| title = A short proof of Sperner's lemma
			\| journal = Journal of Combinatorial Theory
			\| volume = 1 \| issue = 2 \| pages = 299
			\| doi = 10.1016/S0021-9800(66)80035-2 \|mr=0194348 }}.

			*{{citation
			\| last = Meshalkin \| first = L. D.
			\| year = 1963
			\| title = Generalization of Sperner's theorem on the number of subsets of a finite set
			\| journal = Theory of Probability and its Applications
			\| volume = 8 \| issue = 2 \| pages = 203–204
			\| doi = 10.1137/1108023 \|mr=0150049 }}.

			*{{citation
			\| last = Yamamoto \| first = Koichi
			\| year = 1954
			\| title = Logarithmic order of free distributive lattice
			\| journal = Journal of the Mathematical Society of Japan
			\| volume = 6 \| pages = 343–353
			\|mr=0067086 }}.

			{{DEFAULTSORT:Lubell-Yamamoto-Meshalkin inequality}}
			[[Category:Combinatorics]]
			[[Category:Inequalities]]
			[[Category:Order theory]]
			[[Category:Set families]]
			[[Category:Articles containing proofs]]

en>Qwfp: /* Link function */ well spotted. Range (mathematics) is what is meant.

2012-08-16T11:26:14Z

Link function: well spotted. Range (mathematics) is what is meant.

New page

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← Older revision		Revision as of 09:41, 23 February 2014
Line 1:		Line 1:
	~~In [[combinatorics\|combinatorial]] [[mathematics]], the~~ '~~''Lubell–Yamamoto–Meshalkin inequality''', more commonly known as the '''LYM inequality''',~~ is ~~an inequality on the sizes of sets in~~ a ~~[[Sperner family]], proved by {{harvtxt\|Bollobás\|1965}}, {{harvtxt\|Lubell\|1966}}, {{harvtxt\|Meshalkin\|1963}}, and {{harvtxt\|Yamamoto\|1954}}~~. It is ~~named for the initials of three of its discoverers~~.		Friends contact him Royal Seyler. The occupation I've been occupying for years is a bookkeeper but I've already applied for another one. Playing croquet is some thing I will by no means give up. Years ago we moved to Arizona but my wife desires us to move.<br><br>my web site :: [http://Www.Gamersyard.com/profile/eumacdevit extended warranty for cars]

	~~This inequality belongs~~ to ~~the field of [[combinatorics]] of sets, and has many applications in combinatorics. In particular, it can be used~~ to ~~prove [[Sperner's theorem]]. Its name is also used for similar inequalities~~.

	~~==Statement of the theorem==~~
	~~Let ''U'' be an ''n''-element set, let ''A'' be a family of subsets of ''U'' such that no set in ''A'' is a subset of another set in ''A'', and let ''a~~<~~sub~~>k<~~/sub~~>~~'' denote the number of sets of size ''k'' in ''A''. Then~~
	: ~~<math>\sum_{k=0}^n\frac{a_k}{{n \choose k}} \le 1.</math>~~

	~~==Lubell's proof==~~
	~~{{harvtxt\|Lubell\|1966}} proves the Lubell–Yamamoto–Meshalkin inequality by a [[double counting (proof technique)\|double counting argument]] in which he counts the~~ [[permutation]]s of ''U'' in two different ways. First, by counting all permutations of ''U'' directly, one finds that there are ''n''! of them. But secondly, one can generate a permutation of ''U'' by selecting a set ''S'' in ''A'' and concatenating a permutation of the elements of ''S'' with a permutation of the nonmembers. If \|''S''\| = ''k'', it will be associated in this way with ''k''!(''n'' − ''k'')! permutations.
	Each permutation can only be associated with a single set in ''A'', for if two prefixes of a permutation both formed sets in ''A'' then one would be a subset of the other. Therefore, the number of permutations that can be generated by this procedure is
	:~~<math>\sum_{S\in A}\|S\|!(n-\|S\|)!=\sum_{k=0}^n a_k k! (n-k)!.<~~/~~math>~~
	~~Since this number is at most the total number of all permutations,~~
	~~:<math>\sum_{k=0}^n a_k k! (n-k)!\le n!.<~~/~~math>~~
	~~Finally dividing the above inequality by ''n''! leads to the result~~.

	~~== References ==~~

	*{{citation
	~~\| first = B~~. ~~\| last = Bollobás \| authorlink = Béla Bollobás~~
	~~\| title = On generalized graphs~~
	~~\| journal = Acta Mathematica Academiae Scientiarum Hungaricae~~
	~~\| volume = 16 \| issue = 3–4 \| pages = 447–452 \| year = 1965~~
	~~\| doi = 10.1007~~/~~BF01904851 \|mr=0183653 }}.~~

	*{{citation
	~~\| last = Lubell \| first = D.~~
	~~\| year = 1966~~
	~~\| title = A short proof of Sperner's lemma~~
	~~\| journal = Journal of Combinatorial Theory~~
	~~\| volume = 1 \| issue = 2 \| pages = 299~~
	~~\| doi = 10.1016~~/~~S0021-9800(66)80035-2 \|mr=0194348 }}.~~

	*{{citation
	~~\| last = Meshalkin \| first = L. D.~~
	~~\| year = 1963~~
	~~\| title = Generalization of Sperner's theorem on the number of subsets of a finite set~~
	~~\| journal = Theory of Probability and its Applications~~
	~~\| volume = 8 \| issue = 2 \| pages = 203–204~~
	~~\| doi = 10.1137/1108023 \|mr=0150049 }}.~~

	*{{citation
	~~\| last = Yamamoto \| first = Koichi~~
	~~\| year = 1954~~
	~~\| title = Logarithmic order of free distributive lattice~~
	~~\| journal = Journal of the Mathematical Society of Japan~~
	~~\| volume = 6 \| pages = 343–353~~
	~~\|mr=0067086 }}.~~

	~~{{DEFAULTSORT:Lubell-Yamamoto-Meshalkin inequality}}~~
	~~[[Category:Combinatorics]]~~
	~~[[Category:Inequalities]]~~
	~~[[Category:Order theory]]~~
	~~[[Category:Set families]]~~
	~~[[Category:Articles containing proofs]~~]