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Topic: Poset

	poset (Site not responding. Last check: 2007-10-06)
		Examples of posets include the integers and real numbers with their ordinary ordering, subsets of a given set ordered by inclusion, strings ordered lexicographically (as in a phone book), and natural numbers ordered by divisibility.
		Finite posets are most easily visualized as "Hasse diagrams", that is, graphs where the vertices are the elements of the poset and the ordering relation is indicated by edges and the relative positioning of the vertices.
		This can be generalized: any poset can be represented by a directed acyclic graph, where the nodes are the elements of the poset and there is a directed path from a to b if and only if a≤b.
	www.yourencyclopedia.net /Poset.html (850 words)

	PlanetMath: graded poset
		In general poset theory, the rank of a minimal element is 0.
		However, since certain common posets such as the face lattice of a polytope are most naturally graded by dimension, sometimes the rank of a minimal element is required to be
		This is version 4 of graded poset, born on 2004-02-12, modified 2004-04-08.
	planetmath.org /encyclopedia/GradedPoset.html (138 words)

	The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset - Hozo (ResearchIndex)
		The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset - Hozo (ResearchIndex)
		The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset (1995)
		I.Hozo, The eigenvalues of the Laplacian for the homology of the Lie algebra corresponding to a poset, (preprint).
	citeseer.ist.psu.edu /13661.html (771 words)

	Encyclopedia: Poset (Site not responding. Last check: 2007-10-06)
		In mathematics, a partially ordered set (or poset for short) is a set equipped with a special binary relation which formalizes the intuitive concept of an ordering.
		The term ordered set is sometimes also used for posets, as long as it is clear from the context that no other kinds of orders are meant.
		In particular, totally ordered sets can also be referred to as "ordered sets", especially in areas where these structures are more common than posets.
	www.nationmaster.com /encyclopedia/Poset (341 words)

	POSET timing and its application to the synthesis and verification of gate-level timed circuits. (Site not responding. Last check: 2007-10-06)
		POSET timing improves upon geometric methods by utilizing concurrency and causality information to dramatically reduce the number of geometric regions needed to represent the timed state space.
		The POSET timing algorithm can not only efficiently verify the synthesized circuits but also a wide collection of large, highly concurrent timed circuits and systems that could not be previously be verified using traditional techniques.
		POSET timing verification can be used to a general class of specifications which can be translated into a one-safe timed Petri net.
	www.informatik.uni-hamburg.de /TGI/pnbib/m/myers_c_j1.html (299 words)

	[No title]
		As a matter of fact, it is equivalent to the "Poset Conjecture" described in the previous section.
		CASE STUDY: ZIG-ZAG POSETS We conclude with an extended exploration of properties of a family of posets called (for obvious reasons) "zigzag posets".
		For zigzag posets, these are in one-to-one correspondence with alternating permutations of {1,2,3,4,5}, that is, permutations having the pattern a > b < c > d < e...
	www.haverford.edu /math/cgreene/pd/pd6more.html (856 words)

	Order Relation
		The poset of the set of positive real numberes with the less-than-or-equal-to relation is not a well order, because the set itself does not have any least element (0 is not in the set).
		is a graph for a poset which does not have loops and arcs implied by the transitivity.
		To obtain the Hassse diagram of a poset, first remove the loops, then remove arcs < a, b > if and only if there is an element c that < a, c > and < c, b > exist in the given relation.
	www.cs.odu.edu /~toida/nerzic/content/relation/order/order.html (1120 words)

	Help Texts for posets, v2.2
		The procedure does verify that the poset has a minimum element, but does not attempt to verify that P is ranked, or that all maximal elements have the same rank (see 'ranked').
		The output of this computation will be a poset that is isomorphic to the union of P and Q, not necessarily equal to the union of P and Q. In particular, the vertex set of the result will be {1,2,...,p+q} if P has p vertices and Q has q vertices.
		The output of this computation will be a poset that is isomorphic to the ordinal sum of P and Q, but not necessarily equal to the ordinal sum of P and Q. In particular, the vertex set of the result will be {1,2,...,p+q} if P has p vertices and Q has q vertices.
	www.math.lsa.umich.edu /~jrs/software/posetshelp.html (4962 words)

	PlanetMath: poset
		A poset is a partially ordered set, that is, a poset is a pair
		This is version 5 of poset, born on 2001-10-06, modified 2004-02-05.
		Object id is 132, canonical name is Poset.
	planetmath.org /encyclopedia/PartiallyOrderedSet.html (99 words)

	BackgroundMaterial (Site not responding. Last check: 2007-10-06)
		A partially ordered set P (or poset, for short) consists of a ground set X and a reflexive, anti-symmetric and transitive binary relation on X. Such a binary relation is called a partial order.
		A poset which is a chain is also called a total order or a linear order.
		If P is a poset of width w, then P can be partitioned into w chains.
	www.math.gatech.edu /~trotter/Section8-Posets.htm (1040 words)

	online-judge.uva.es :: View topic - width of a POSET (Site not responding. Last check: 2007-10-06)
		This is related to the width of the poset (clearly the width is a lower bound for the number of chains in the partition), but I'm not sure whether it has to be the same value.
		I think that determining the width of a poset is hard (in the general case), however, Dilworth's lemma (http://mathworld.wolfram.com/DilworthsLemma.html) may be of some help.
		I realised after I posted that as the dimension of this poset in the question is 2 there may be some special way than a generalized algorithm.
	online-judge.uva.es /board/viewtopic.php?t=6988&sid=339d3b73d09075dabc1edb063a703b5e (343 words)

	Conjugacy Classes of Subgroups
		The elements of the poset correspond to the conjugacy classes of subgroups.
		Given poset elements e and f, return the poset element that corresponds to the class of subgroups that contains the centralizers of the subgroups of class f (taken in a subgroup of class e).
		Given poset elements e and f, return the poset element that corresponds to the class of subgroups that contain the normalizers of the subgroups of class f (taken in a subgroup of class e).
	www.math.uiuc.edu /Software/magma/text174.html (2372 words)

	(Denford M., Solomon A., Leaney J., O'Neill T.) Architectural Abstraction as Transformation of Poset Labelled Graphs (Site not responding. Last check: 2007-10-06)
		A model of system architectures and architectural abstraction is proposed, using poset labelled graphs and their transformations.
		The poset labelled graph formalism closely models several important aspects of architectures, namely topology, type and levels of abstraction.
		The technical merits of the formalism are discussed in terms of the ability to express and use domain knowledge to ensure sensible refinements.
	www.jucs.org /jucs_10_10/architectural_abstraction_as_transformation (163 words)

	PROMYS
		A poset (partially-ordered set) is a mathematical object satisfying a few simple properties, and any poset can be turned into a two-player game.
		Byrnes developed a new theorem, the Poset Game Periodicity Theorem, which concerns general poset games: as a poset expands in two directions, periodic patterns emerge in the associated poset game not only in losing positions, but also in positions with any fixed g-value (g-values are a general classification of game positions.) Using his theorem, Mr.
		We prove a general theorem about poset games, which we call the Poset Game Periodicity Theorem: as a poset expands along two chains, losing positions and positions with any fixed g-value have a periodic pattern.
	www.promys.org /community/byrnes.html (376 words)

	Intel STS Results \| Science Service
		In particular, if P is an infinite poset of finite width, then all its homology groups are finitely generated, and the sum above converges.
		Finally, to prove Theorem 2 in the infinite case, we suppose some counterexample exists. With the aid of the lemma, we find a finite subposet which also violates the theorem, and this is already known to be a contradiction.
		We also prove Corollary 1. In the finite case, it readily holds by letting w go to infinity in Theorem 2. If P is infinite, we again show that any poset violating the corollary must have some finite subposet violating the corollary, which is impossible.
	www.sciserv.org /sts/60sts/report_carroll.asp (366 words)

	Definition of d-Complete Poset (Site not responding. Last check: 2007-10-06)
		is the poset obtained by removing the maximal element of d
		(1) poset and which cannot be extended to form an interval which is a d
		A poset P is said to be d
	www.math.unc.edu /Faculty/rap/DfndC.html (402 words)

	[No title]
		Immediate predecessor which is not reflexive, symmetric or transitive is defined on a poset, this means that it implies an underlying partial ordering.
		For a and b in a poset [S,<] a least upper bound or join or sum of a and b is an element of c of S satisfying the relationship a < c and b < c.
		A poset whose any two elements have unique join and meet is called a lattice.
	www.cmpe.boun.edu.tr /~gurgen/cmpe220/topics/chapter6.htm (350 words)

	Math Trek: Chomping to Win, Science News Online, March 22, 2003 (Site not responding. Last check: 2007-10-06)
		A poset, or partially ordered set, is a set of elements in which some elements are smaller than other elements but not every pair of elements can necessarily be compared.
		One example of a poset consists of an integer and all its positive divisors (excluding 1).
		For instance, the positive divisors of 42 are 2, 3, 6, 7, 14, and 21, and the associated poset is designated {2, 3, 6, 7, 14, 21, 42}.
	www.sciencenews.org /20030322/mathtrek.asp (1002 words)

	[No title]
		We illustrate both methods by constructing the poset of subsets of 1...N whose sum is even, for N=5 and N=7.
		Since A is the bottom element of the poset, may also be described as the principal order ideal generated by B. Build[SetP[5],setp5] Building poset setp5...
		Since both P and the chain are indexed by 1...n, we may represent such a map by a permutation of 1...n.
	www.haverford.edu /math/cgreene/pd/pd4ops.html (973 words)

	Sergei Bezrukov (research interests)
		Having this theory in hands and combining it with some extremal poset problems I have shown that all known results on the EIP for particular graph families known so far, are special cases of my approach.
		Among such results is a solution of the SMP for the poset of all words of a binary alphabet ordered by the subword relation and the poset of linear subspaces of PG(n,2) ordered by inclusion (joint research with A.
		Sali we study the poset of submatrices of a matrix and also some other kinds of poset products.
	mcs.uwsuper.edu /sb/interests.html (1274 words)

	Poset (Site not responding. Last check: 2007-10-06)
		A set with a partial order is called partially ordered set, or poset for short.
		The termordered set is sometimes also used for posets, as long as it is clear from the context that no other kinds oforders are meant.
		In particular, totally ordered sets canalso be referred to as "ordered sets", especially in areas where these structures are more common than posets.
	www.therfcc.org /poset-211387.html (212 words)

	Dr. Hsu's Abstract (Site not responding. Last check: 2007-10-06)
		In this talk a method of global analysis of nonlinear dynamical systems based upon the poset theory is introduced.
		The main purpose of the talk is, however, to discuss how the poset theory can be linked to nonlinear dynamical systems and cell mapping and in what ways this linkage can facilitate the analysis of the complex global behavior of such systems.
		It will also be shown that the poset theory offers a new way of characterizing and classifying nonlinear dynamical systems.
	www.me.gatech.edu /me/events/seminars/HsuAbs.html (119 words)

	Poset representation and similarity comparisons of systems in IR (ResearchIndex)
		Abstract: In this paper we are using the poset representation to describe the complex answers given by IR systems after a clustering and ranking processes.
		The answers considered may be given by cartographical representations or by thematic sub-lists of documents.
		The poset representation, with the graph theory and the relational representation opens many perspectives in the definition of new similarity measures capable of taking into account both the clustering and ranking processes.
	citeseer.ist.psu.edu /651594.html (192 words)

	The Linear Extension Diameter of a Poset
		The Linear Extension Diameter of a Poset: SIAM Journal on Discrete Mathematics Vol.
		The distance between two permutations of the same set X is the number of pairs of elements that are in different order in the two permutations.
		Given a poset $P=(X,\leq)$, a pair $L_1,L_2$ of linear extensions is called a diametral pair if it maximizes the distance among all pairs of linear extensions of P.
	epubs.siam.org /sam-bin/dbq/article/32613 (315 words)

	MATHS: Orders
		In all posets, the minima(maxima) are among the least (greatest) and if there exist any minima(maxima) then there can only be one of them.
		In a general poset none of the optima have to exist.
		Consider any map from an poset to itself then some points wil increase when the map is applied and some will decreas and some will not change.
	www.csci.csusb.edu /dick/maths/math_21_Order.html (3010 words)

	Enumerating the Ideals of a Poset (ResearchIndex)
		Abstract: An enumeration of the ideals of a poset can be used to solve various scheduling and reliability problems.
		Current algorithms for generating ideals require an amortized time of O(n) per ideal in the worst case, where n is the number of elements in the poset.
		In this paper, an algorithm is given which generates ideals in an amortized time of O(log n) per ideal.
	citeseer.ist.psu.edu /465417.html (287 words)

	Basic Poset Stuff (Site not responding. Last check: 2007-10-06)
		Poset is short for "partially ordered set." If x and y are elements of a poset P, then we say that y covers x if y > = x and there are no elements between x and y.
		One begins to draw a version of the order (or Hasse) diagram of P by choosing a maximal element z and depicting it with a dot.
		A poset P is said to be connected if its order diagram is connected.
	www.math.unc.edu /Faculty/rap/Basic.html (179 words)

	The Coset Poset And Probabilistic Zeta Function Of A Finite Group - Brown (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		We investigate the topological properties of the poset of proper cosets xH in a finite group G. Of particular interest is the reduced Euler characteristic, which is closely related to the value at \Gamma1 of the probabilistic zeta function of G. Our main result gives divisibility properties of this reduced Euler characteristic.
		Introduction For a finite group G and a non-negative integer s, let P (G; s) be the probability that a randomly chosen ordered s-tuple from G generates G. Philip...
		K.S. Brown, The coset poset and probabilistic zeta function of a finite group.
	citeseer.lcs.mit.edu /brown99coset.html (465 words)

	The Spider Poset is Macaulay - Bezrukov, Elsasser (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		Abstract: Let Q(k; l) be a poset whose Hasse diagram is a regular spider with k+1 legs having the same length l (cf.
		We show that for any n 1 the n th cartesian power of the spider poset Q(k; l) is a Macaulay poset for any k 0 and l 1.
		In combination with our recent results [2] this provides a complete characterization of all Macaulay posets which are cartesian powers of upper semilattices, whose Hasse diagrams are trees.
	citeseer.lcs.mit.edu /bezrukov98spider.html (515 words)

	Poset Ontologies and Concept Lattices as Semantic Hierarchies (ResearchIndex) (Site not responding. Last check: 2007-10-06)
		Poset Ontologies and Concept Lattices as Semantic Hierarchies (ResearchIndex)
		Poset Ontologies and Concept Lattices as Semantic Hierarchies
		Our approach depends on casting the GO as a labeled partially ordered set (poset) [16], and then using scores based...
	sherry.ifi.unizh.ch /637828.html (372 words)

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