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Topic: Sperner family

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	Family
		Knott family of lighthouse keepers The Knott family of lighthouse keepers are accredited with the longest period of cont...
		Lowell family The Lowell family is a Massachusetts.
		Saltonstall family The Saltonstall family is a Salem Witch Trials—graduated in 1659.
	www.brainyencyclopedia.com /topics/family.html (4120 words)

	Sperner family -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		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)

	[No title] (Site not responding. Last check: 2007-10-08)
		The fact that it does give the smallest possible number is Sperner's theorem, not to be confused with the other Sperner's theorem (or lemma) which is about triangulations.
		Sperner's theorem is usually stated in the following equivalent way: the maximum size of a family of incomparable subsets of a k-element set is C(k,INT(k/2)).
		Sperner's theorem is discussed in many textbooks on combinatorics; you should have no trouble finding it.
	www.math.niu.edu /~rusin/known-math/98/sperners (285 words)

	[No title]
		] A family of fungi of the order Sphaeropsidales in which the pycnidia are fl or dark-colored and are flask-, cone-, or lens-shaped with thin walls and a round, relatively small pore.
		] A family of myodarian cyclorrhaphous dipteran insects in the subsection Acalypteratae.
		] A family of isopod crustaceans in the suborder Flabellifera in which the body is broad and oval and the inner branch of the uropod is immovable.
	www.accessscience.com /Dictionary/S/S43/DictS43.html (2460 words)

	PlanetMath: LYM inequality
		This inequality is known as LYM inequality by the names of three people that independently discovered it: Lubell[2], Yamamoto[4], Meshalkin[3].
		Sperner theory, volume 65 of Encyclopedia of Mathematics and Its Applications.
		Generalization of Sperner's theorem on the number of subsets of a finite set.
	planetmath.org /encyclopedia/LYMInequality2.html (113 words)

	Spahr Family Crest
		First found in the Rhineland, where this family was a prominent contributor to the development of the district from ancient times.
		In continental Europe, the most ancient recorded family crest was discovered upon the monumental effigy of a Count of Wasserburg in the church of St. Emeran, at Ratisobon, Germany...
		No families, not even the royal houses, can make sound claim to the right to bear arms unless a proven connection is established through attested Genealogical records...
	www.houseofnames.com /xq/asp.fc/qx/spahr-family-crest.htm (454 words)

	The world's top sperner s lemma websites
		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 pointss, and in root-finding algorithms.
	dirs.org /wiki-article-tab.cfm/sperner_s_lemma (622 words)

	Abstract for 2001/12/6: (Site not responding. Last check: 2007-10-08)
		Sperner's inequality concerns the set P(S) consisting of all subsets of a finite set S, partially ordered by subset inclusion.
		In 1928, Sperner found a bound (in terms of the size of S) for the size of an antichain, that is, a subset of P(S) in which there are no nontrivial chains.
		His result was generalized in two different directions: About 25 years later, Erdös extended Sperner's inequality to r-systems, that is, subsets of P(S) in which chains contain at most r elements.
	www.math.binghamton.edu /dept/ComboSem/abstract.200012beck.html (174 words)

	Families of Sets with Locally Bounded Width - Knill (ResearchIndex)
		Abstract: A family of sets F is locally k-wide if and only if the width (as a poset ordered by inclusion) of F x = fU 2 F j x 2 Ug is at most k for every x.
		The directed covering graph of a locally 1-wide family of sets is a forest of rooted trees.
		The proof involves a counting argument based on families of closed sets associated with the Sperner closures in the filters of F.
	citeseer.ist.psu.edu /10730.html (436 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.
		NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
	www.nrich.maths.org.uk /public/viewer.php?obj_id=1383 (763 words)

	James B. Shearer - kcst abstract (Site not responding. Last check: 2007-10-08)
		Abstract: A family F of subsets of an n-set S is said to have property X for a k-coloring of S if for all A,B contained in F such that A is not a subset of B, B-A is not monochromatic.
		Let f(n,k) denote the maximum value of F over all families F which have property X with respect to some k-coloring of S. The standard and two-part Sperner Theorems imply that f(n,1)=f(n,2)=binomial coefficient n choose [n/2].
		A natural generalization of Sperner's theorem concerning the existence of nice extremal families F is proved.
	www.research.ibm.com /people/s/shearer/abstracts/kcst.html (187 words)

	[No title]
		We establish sufficient conditions for the existence of a family of positive and monotone solutions at resonance.
		Our approach is based on the Sperner's Lemma, proposing in this way an alternative to the classical methodologies based on fixed point or degree theory and results the introduction of a new set of quite natural hypothesis.
		It is worth noticing that the use of Sperner's Lemma in this study, gives an alternative to the usual considerations of topological methods, such as fixed point theories, and results to more strongly conclusions under possibly weaker but in any case much different assumptions.
	www.ma.hw.ac.uk /EJDE/Volumes/2004/25/palamides-tex (1858 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Generalizing this result for Sperner hypergraphs, we can show a similar statement, replacing the notion of "induced matching" with a "special binary tree" built from the hyperedges.
		More generally, let us consider a polymatroid set function f (nonnegative, monotone, submodular, integer valued) over a finite set V, the family A(t) of all minimal subsets S of V, for which f(S)≥t, and the family B(t) consisting of all maximal subsets for which f(S)<t.
		Moreover, for any Sperner hypergraph H there are polymatroid set functions f, for which H=A(t), for some integer threshold t.
	www.ecp6.jussieu.fr /seminaire/resumes/0001/010517b.html (180 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		We present an alternative formalism for separation of duty policies based on antichains in a powerset (Sperner families), and show that it is no less expressive than existing approaches.
		This lattice provides the formal framework for a family of secure access control models which incorporate the advantages of existing paradigms without introducing many of their respective disadvantages.
		The RHA family of models provides a useful alternative to the RRA97 sub-model of ARBAC97 which is used to control updates to the role hierarchy.
	www.isg.rhul.ac.uk /~jason/Abstracts/abstracts.html (3871 words)

	Variant of Sperner's lemma (Site not responding. Last check: 2007-10-08)
		The answer is at least (n/2 choose n/4): Group the elements into n/2 pairs, glue every such pair together, and consider all cardinality-n/4 subsets of the set of glued pairs.
		Here's a different argument that produces a much larger family, within a polynomial factor of optimal: form a graph the vertices of which are the (n choose n/2) subsets of cardinality n/2, with edges connecting pairs that differ in only two items.
		I am interested in the following variant of Sperner's lemma: How large is the largest family F of subsets of {1,...,n}, where for each A,B in F, both B\A and A\B have cardinality at least two?
	www.forum-one.org /new-6326728-4346.html (421 words)

	[No title]
		Let $M(n,t)$ and $M_{\le k}(n,t)$ be the maximum size of a $t$--intersecting family in $2^{[n]}$ and ${[n] \choose \le k}$, respectively.
		For every Sperner family $S$ over $\Omega$ there exists a relation whose set of minimal keys equals $S$, called an Armstrong relation for $S$.
		Zsolt Katona, E\"otv\"os University, Budapest TALK: Intersecting families of sets, no $l$ containing two common elements abstract: Let $H$ denote the set $\{f_1,f_2,...,f_n\}$, $2^{[n]}$ the collection of all subsets of $H$ and $\F\subseteq 2^{[n]}$ be a family.
	www.math-inst.hu /~extremal/titles.txt (2554 words)

	Schechter: papers
		We construct a family of Banach spaces whose bounded sets are precisely the subsets of KH[0,1] that are equiintegrable and pointwise bounded.
		This article shows that those four formulas have different effects when added to relevant logic, and then lists many formulas that have the same effect as positive paradox or mingle.
		Abstract: Brouwer's Fixed Point Theorem and related theorems (Schauder, Kakutani, etc.) are proved using a topological argument (e.g., compactness) together with a combinatorial argument (e.g., Sperner's Lemma).
	math.vanderbilt.edu /~schectex/papers (1181 words)

	14th Cumberland Conference - Abstracts (Site not responding. Last check: 2007-10-08)
		We discuss Hall's condition for a proper "multicoloring" of a graph G whose vertices are assigned measurable sets from a measure space (and positive real numbers prescribing color set sizes), and pose a problem or two.
		is an integer, then the average size of the members of the family is at least k.
		Stanley showed that M(n) has the Sperner property and is rank unimodal, but open questions remain, for example it is open whether M(n) has a symmetric chain decomposition.
	www.msci.memphis.edu /~balistep/Abstracts.html (2984 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		This theorem stimulated the development of a fast growing theory dealing with extremal problems on finite sets and, more generally, on finite partially ordered sets.
		This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming (e.g.
		Studying Sperner theory means learning many important techniques in discrete mathematics and combinatorial optimization on a particular theme.
	elib.zib.de /pub/opt-net/publications/books/v97w16n2 (84 words)

	Sporrer Family Crest
		When did the Sporrer family first arrive in the United States?
		We have researched the Sporrer family crest in the most recognized sources.
		We encourage you to study the Sporrer genealogy to find out if you descend from someone who bore a particular family crest.
	www.houseofnames.com /xq/asp.fc/qx/sporrer-family-crest.htm (454 words)

	Sperner Theory - Cambridge University Press (Site not responding. Last check: 2007-10-08)
		The starting point of this book is Sperner’s theorem, which answers the question: What is the maximum possible size of a family of pairwise (with respect to inclusion) subsets of a finite set?
		This theorem stimulated the development of a fast growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets.
		This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics.
	www.cup.cam.ac.uk /aus/catalogue/catalogue.asp?isbn=0521452066 (139 words)

	SAT Workshop, Siena
		A hypergraph H is a pair (V,E) of a finite set V and a family E = {E1,...
		A simple hypergraph is also known as a Sperner family.
		The transversal hypergraph of H is the hypergraph Tr(H) = (V, F) such that F is the family of all minimal (w.r.t.
	www.ececs.uc.edu /~franco/Sat-workshop/sat-workshop-open-problems.html (1684 words)

	Personal Report: Nina Sperner (Site not responding. Last check: 2007-10-08)
		I won't write about my family here, because I wouldn't be able to describe how nice they were to me anyway and I also don't want to tell you how much I was impressed by everything we saw and experienced, because it simply was too much.
		As everybody knows, Americans have a lot of curious and remarkable attitudes.They always eat pizza and hardly ever cook by themselves, despite that, they love fat free products, because they are crazy about their shape, the TV is running all the time as well as the telephone never stops ringing.
		All that stuff didn't hinder us from making good new friends and I'm really excited to read the Americans' report after they have been here.
	home.foni.net /~rippe/pers17.htm (279 words)

	RootsWeb: GEN-DE-L Sperner Family (Site not responding. Last check: 2007-10-08)
		I am looking for any information about the family of Alfons Sperner their home
		The surviving daughter does not know how her father was killed or if and where
		The daughter of Alfons Sperner Gerlind B Sperner was born in
	archiver.rootsweb.com /th/read/GEN-DE/1998-09/0905651153 (60 words)

	On a Covering Property of Maximal Sperner Families (ResearchIndex)
		On a Covering Property of Maximal Sperner Families (ResearchIndex)
		Abstract: In the lattice of subsets of an n-set X, every maximal Sperner family S may be partitioned into disjoint subfamilies A and B, such that the union of the upset of A with the downset of B yields the entire lattice: U(A) [ D(B) = 2.
		1.4: On the structure of maximum 2-part Sperner families - Shahriari (1995)
	citeseer.ist.psu.edu /555021.html (218 words)

	SPERNER surnames
		5 names of the SPERNER surnames are in the One Great Family Tree.
		To see SPERNER surnames sign up now for our 7-day FREE Trial.
		Within minutes you can be viewing all SPERNER surnames information in the OneGreatFamily Tree.
	www.onegreatfamily.com /surname/Sperner.html (93 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		(who) Maria Chudnovsky (Technion) will talk about (what) Systems of Disjoint Representatives Abstract: --------- Let F be a family of hypergraphs on the same vertex set.
		We are going to formulate sufficient conditions for F to have a system of disjoint representatives, which is a choice of edges from every hypergraph in the family in such a way that edges chosen from different hypergraphs would be disjoint.
		In the course of the proof special triangulations of the simplex are constructed and Sperner's lemma is used.
	www.math.technion.ac.il /~techm/19991128141519991128chu (222 words)

	14th Cumberland Conference - Schedule of Talks (Site not responding. Last check: 2007-10-08)
		On the average size of sets in an intersecting Sperner family
		Decomposition dimension of graphs and union-free families of sets
		On the existence of Hamiltonian paths in the cover graph of M(n)
	www.msci.memphis.edu /~balistep/Schedule.html (149 words)

	standard (Site not responding. Last check: 2007-10-08)
		(a) no X_i is a subset of any X_j (Sperner condition) for any i <> j,
		1) a maximal family contains sets with size <= [(n-1)/2] only and
		2) if there is at least one 1-element set then we get the size of the family given above if n is even and it's not maximal if n is odd (n<>7).
	forumgeom.fau.edu /POLYA/Inventory/Inventory018.html (200 words)

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