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	Emanuel Sperner - Wikipedia, the free encyclopedia
		Emanuel Sperner (9 December 1905 - 31 January 1980) was a German mathematician, best known for two theorems.
		The Sperner theorem, from 1927, says that the number of antichains in the power set of an n-set is at most the middle binomial coefficient(s).
		Sperner's lemma, from 1924, states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.
	en.wikipedia.org /wiki/Emanuel_Sperner (169 words)

	Emanuel Sperner -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-29)
		Emanuel Sperner (9 December 1905 - 31 January 1980) was a (A person of German nationality) German (A person skilled in mathematics) mathematician, best known for two (An idea accepted as a demonstrable truth) theorems.
		The (additional info and facts about Sperner theorem) Sperner theorem, from 1927, says that the number of antichains in the (additional info and facts about power set) power set of an n-set is at most the middle (additional info and facts about binomial coefficient) binomial coefficient(s).
		It was later noticed that this lemma provides a direct proof of the (additional info and facts about Brouwer fixed-point theorem) Brouwer fixed-point theorem without explicit use of (The quality of being similar or corresponding in position or value or structure or function) homology.
	www.absoluteastronomy.com /encyclopedia/e/em/emanuel_sperner.htm (231 words)

	Sperner's lemma - Wikipedia, the free encyclopedia
		In combinatorial mathematics, Sperner's lemma states that every Sperner coloring of a triangulation of an n-dimensional simplex contains a cell colored with a complete set of colors.
		The initial result of this kind was proved by Emanuel Sperner, in relation with proofs of invariance of domain.
		Sperner colorings have been used for effective computation of fixed points, in root-finding algorithms, and are applied in fair division algorithms.
	en.wikipedia.org /wiki/Sperner's_lemma (551 words)

	Sperner family -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-29)
		In (additional info and facts about combinatorics) combinatorics, a Sperner family (or Sperner system), named in honor of (additional info and facts about Emanuel Sperner) Emanuel Sperner, is a (additional info and facts about set system) set system (F, E) in which no element is contained in another.
		Equivalently, a Sperner family is an (additional info and facts about antichain) antichain in the inclusion (Framework consisting of an ornamental design made of strips of wood or metal) lattice over the (additional info and facts about power set) power set of E.
		Sperner's theorem can be seen as a special case of (additional info and facts about Dilworth's theorem) Dilworth's theorem.
	www.absoluteastronomy.com /encyclopedia/s/sp/sperner_family.htm (254 words)

	PlanetMath: Sperner's theorem
		A family satisfying the conditions of Sperner's theorem is usually called Sperner family or antichain.
		Sperner theory, volume 65 of Encyclopedia of Mathematics and Its Applications.
		This is version 4 of Sperner's theorem, born on 2003-08-17, modified 2005-01-01.
	planetmath.org /encyclopedia/SpernersTheorem.html (173 words)

	Sperner family - TheBestLinks.com - Combinatorics, Lattice, Power set, Antichain, ...
		Sperner family, Combinatorics, Lattice, Power set, Antichain, Emanuel Sperner...
		In combinatorics, a Sperner family (or Sperner system), named in honor of Emanuel Sperner, is a set system (F, E) in which no element is contained in another.
		Equivalently, a Sperner family is an antichain in the inclusion lattice over the power set of E.
	www.thebestlinks.com /Sperner_family.html (260 words)

	Emanuel Sperner (Site not responding. Last check: 2007-10-29)
		Emanuel Sperner (9 December 1905 - 31 January 1980) was a German mathematician knownfor his two lemmas.
		The two Sperner's lemmas are both combinatorial in nature.
		Oneof them (from 1932) is a step in a direct proof of the Brouwer fixed-point theorem without explicit use of homology.
	www.therfcc.org /bbs1/messages/emanuel-sperner-239461.html (132 words)

	Emanuel Steward Definition / Emanuel Steward Research (Site not responding. Last check: 2007-10-29)
		Emanuel Steward (born 1944 Events World War II January January 4 - The Battle of Monte Cassino begins.
		Emanuel Steward is the premier trainer/manager in boxing today.
		Emanuel Steward is the man behind the Kronk Gym and it's 27 world champions.
	www.elresearch.com /Emanuel_Steward (463 words)

	Emanuel Sperner (Site not responding. Last check: 2007-10-29)
		Emanuel Sperner (9 December 1905 - 31 January 1980) was a German mathematician known for his two lemmas.
		He was born in Waltdorf (near Nysa, now in Poland), and died in Salzburg-Laufen.
		One of them (from 1932) is a step in a direct proof of the Brouwer fixed-point theorem without explicit use of homology.
	www.sciencedaily.com /encyclopedia/emanuel_sperner (194 words)

	Science Fair Projects - Talk:Emanuel Sperner
		Sperner called his antichain result a "Satz", in the very title of his paper.
		As it is, I've never actually seen his Satz called his lemma before this.
		In fact, I just noticed that the antichain link refers to Sperner family, which contains a proof of "Sperner's theorem".
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Talk:Emanuel_Sperner (304 words)

	nrich.maths.org::Mathematics Enrichment::Sperner's Lemma
		This is Sperner's Lemma, named after its discoverer Emanuel Sperner, a 20th century German mathematician.
		Sperner's Lemma is a key result in topology.
		Since the circled numbers are either 3 (for a small triangle labelled ABC counterclockwise) or -3 (for a small triangle labelled ABC clockwise), the number of counterclockwise triangles must be exactly one more than the number of clockwise triangles.
	www.nrich.maths.org.uk /public/viewer.php?obj_id=1383 (763 words)

	Read This: How the Other Half Thinks
		Label each vertex of the triangulation by a, b, or c, in such a way that vertices on edge xy of T must be labelled either x or y.
		Sperner's lemma (Emanuel Sperner, 1928) states that there is at least one small triangle in the triangulation whose vertices have all three labels.
		There is a photograph of Sperner on p.
	www.maa.org /reviews/otherhalf.html (2780 words)

	Science Fair Projects - Sperner family
		Since S is an antichain, we can sum over the above inequality from k = 0 to n and then apply the LYM inequality to obtain
		Sperner's theorem can be seen as a special case of Dilworth's theorem.
		It is sometimes called Sperner's lemma, but unfortunately, this name also refers to another result on coloring.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Sperner_family (355 words)

	Families of Sets with Locally Bounded Width - Knill (ResearchIndex) (Site not responding. Last check: 2007-10-29)
		It is shown that if F is a locally k-wide family of subsets of f1; : : : ; ng, then jF j (2k) k\Gamma1 n.
		The proof involves a counting argument based on families of closed sets associated with the Sperner closures in the filters of F.
		Knill, Families of sets with locally bounded width, Los Alamos National Laboratory report LA-UR-93-300, 1993; to appear in Graphs and Combinatorics.
	citeseer.ist.psu.edu /10730.html (436 words)

	[No title]
		Kerstjens-Frederikse WS, Kurahashi H, Driscoll DA, Budarf ML, Emanuel BS, Beatty B, Scheidl T, Siegel-Bartelt J, Henderson K, Cytrynbaum C, Nie G, and Teshima I. Microdeletion 22q11.2: clinical data and deletion size.
		Colombo R, Bignamini AA, Carobene A, Sasaki J, Tachikawa M, Kobayashi K, Toda T. Age and origin of the FCMD 3｢-untranslated-region retrotransposal insertion mutation causing Fukuyama-type congenital muscular dystrophy in Japanese population.
		Kurahashi H, Inagaki H, Yamada K, Ohye T, Taniguchi M, Emanuel BS, Toda T. Cruciform DNA structure underlies the etiology for palindrome-mediated human chromosomal translocations.
	www.clgene.med.osaka-u.ac.jp /www/gyoseki.html (4850 words)

	The Mathematics Genealogy Project - Emanuel Sperner (Site not responding. Last check: 2007-10-29)
		Click here to see the students listed in chronological order.
		According to our current on-line database, Emanuel Sperner has 22 students and 145 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=21626 (109 words)

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