
	Where results make sense

Topic: Partially ordered set

Related Topics

Order biology

orders of magnitude

Orders of magnitude mass

Order of the British Empire

Order of the Garter

order of precedence

Harry Potter and the Order of the Phoenix

Orders of magnitude power

Order of Canada

total order

Orders of magnitude length

Order of the Bath

In the News (Tue 2 Dec 08)

Damian Green

Sumner Redstone

Crimson Tide

Tommy Tuberville

Bill Clinton

Wayne Rooney

Vilasrao Deshmukh

Wake Forest

Grand Slam

Oklahoma State

	Partially ordered set - Wikipedia, the free encyclopedia
		In mathematics, especially order theory, a partially ordered set (or poset for short) is a set equipped with a partial order relation.
		A partial order is a binary relation R over a set P which is reflexive, antisymmetric and transitive.
		The set of subsets of {x,y,z}, ordered by inclusion
	en.wikipedia.org /wiki/Partially_ordered_set (535 words)

	Partial order
		In mathematics, a partial order ≤ on a set X is a binary relation that is reflexive, antisymmetric and transitive, i.e., it holds for all a, b and c in X that:
		A subset of a partially ordered set inherits a partial order.
		Since the intersection of partial orders on a given set X is again a partial order on X, every relation R on X generates a unique partial order on X, the smallest partial order containing R.
	www.ebroadcast.com.au /lookup/encyclopedia/po/Poset.html (777 words)

	Talk:Partially ordered set - Wikipedia, the free encyclopedia
		Unlike a total ordering, a partial ordering need not guarantee the mutual comparability of all objects in the set.
		For example, we could define an ordering ⊆ on the set of all political organizations such that a⊆b if every member of a is also a member of b.
		In a partially ordered set that is not totally ordered, there is at least one pair of members a and b for which neither aRb nor bRa is true.
	en.wikipedia.org /wiki/Talk:Partially_ordered_set (1234 words)

	Ordered Sets : Software Foundations : Thomas Alspaugh : UCI
		It is usually clear by context whether "order" refers literally to an order (an order relation) or by synechdoche to an ordered set.
		This set is partially ordered, because not all classes in the set are related by the subclass relations (for example, Vector and HashSet are not related and are thus incomparable: Vector
		Then the ordered set of the positive integers to 15 ordered by the converse of divides (now with the divident considered "higher" than the dividend), is the dual Q∂ of Q.
	www.ics.uci.edu /~alspaugh/foundations/orderedSet.html (2579 words)

	Equivalence Relation
		The relation r is a partial ordering on the set s, or s is a partially ordered set via r, or s is a poset, if r is transitive and antisymmetric.
		A lattice is a partial ordering with a lub and a glb for every pair of points.
		A linear ordering, or total ordering, is a partial ordering where all pairs of elements are comparable.
	www.mathreference.com /set,rst.html (1118 words)

	PlanetMath: directed set (Site not responding. Last check: 2007-11-07)
		A directed set is a partially ordered set
		Cross-references: property, antisymmetric, iff, residual, subset, partially ordered set
		This is version 3 of directed set, born on 2002-08-01, modified 2003-02-08.
	planetmath.org /encyclopedia/DirectedSet.html (65 words)

	Mathematical Programming Glossary - P (Site not responding. Last check: 2007-11-07)
		The set packing problem is the question, "Does a collection of sets contain at least K mutually disjoint subsets?" (K is a positive integer not greater than the number of sets given.) This is solvable in polynomial time if no set has more than 2 members.
		The set X^0 depends on the type of penalty function, and there are two classical types, each requiring P to be continuous: interior (or barrier) and exterior.
		Let N be a finite set and let f be a submodular function on the subsets of N with f(Ø)=0.
	carbon.cudenver.edu /~hgreenbe/glossary/P.html (4004 words)

	PlanetMath: poset (Site not responding. Last check: 2007-11-07)
		A poset is a partially ordered set, that is, a poset is a pair
		In a partial order, not any two elements need to be comparable.
		Cross-references: subsets, comparable, inclusion, relation, power set, integers, relation on, partial order
	planetmath.org /encyclopedia/Poset.html (99 words)

	EE290N Lecture 9 Notes
		In an ordered signal process network, T(s) is totally ordered for each signal s but the set of all tags T(ss) is typically partially ordered.
		The output signal preserves the ordering of the tokens of the input signals, but there is no ordering between tokens of different input signals.
		Given a set of signals S and a partially order relation E, (S,E) is a partially ordered set or POSET.
	ptolemy.eecs.berkeley.edu /~eal/ee290n/lecture9/lec9.html (568 words)

	Ordered and Well-Ordered Set (Site not responding. Last check: 2007-11-07)
		A set S is called partially ordered if there exists a relation r (usually denoted by the symbol
		A set S is called ordered if it is partially ordered and every pair of elements x and y from the set S can be compared with each other via the partial ordering relation.
		A set S is called well-ordered if it is an ordered set for which every non-empty subset contains a smallest element.
	pirate.shu.edu /projects/reals/infinity/defs/ordering.html (85 words)

	Generalized Polymatroids on Partially Ordered Sets
		Ordered polymatroids are defined by submodular rank functions with respect to the set of all antichains of a finite partially ordered set (poset).
		The Core-Polytope ${\rm Core (f)}$ of an ordered polymatroid ${\rm P} (f)$ related to a submodular function $f$ consists of all elements with maximal cardinality and does not coincide with the set ${\rm Max} (f)$ of all maximal elements of ${\rm P} (f)$.
		The set ${\rm Max} (f)$ is not a polyhedral set in general.
	dmawww.epfl.ch /roso.mosaic/ismp97/ismp_abs_105.html (282 words)

	Notation
		A set V (a, b, c,) is called a partially ordered set when a strict partial order relation"a" is defined on it.
		A partially ordered set is denoted by (A; p)
		In other words, an ordered set is a partially ordered set with additional equivalence relation defined on it, and where the conditions "neither ap b" nor bp a" and "a ≈ b" are equivalent.
	www.unesco.org /webworld/idams/advguide/Chapt2_2_2.htm (386 words)

	b_posets
		Give an example of a map between partially ordered sets that is isotone, one-to-one, and onto, but not an isomorphism.
		be a partially ordered set in which every chain is finite and every antichain is finite.
		A bipartite graph is a partially ordered set of the kind used in Hall's matching theorem, where all elements are maximal or minimal but not both.
	www.math.ucla.edu /~baker/222a/handouts/b_posets/node4.html (415 words)

	Mathematical Structures: Partially ordered sets (Site not responding. Last check: 2007-11-07)
		A partially ordered set (also called ordered set or poset for short) is a structure P = (P, ≤) such that P is a set and ≤ is a binary relation on P that is
		A strict partial order is a structure (P, <) such that P is a set and < is a binary relation on P that is
		Any poset is order-isomorphic to a poset of subsets of some set, ordered by inclusion.
	math.chapman.edu /cgi-bin/structures.pl?Partially_ordered_sets (215 words)

	Zorn's lemma : Zorns lemma (Site not responding. Last check: 2007-11-07)
		Zorn's Lemma, also known as the Kuratowski-Zorn Lemma, is a theorem of set theory that states that:Every partially ordered set, in which every chain (i.
		Then there exists a partially ordered set, or poset, P such that every totally ordered subset has an upper bound, and every element has a bigger one.
		In fact, the sequence is too long for the set P; there are too many ordinals, more than there are elements in any set, and the set P will be exhausted before long and then we will run into the desired contradiction.
	www.termsdefined.net /zo/zorns-lemma.html (955 words)

	g_distrib
		As you know, a maximal chain in a partially ordered set is a chain that is not contained in any other chain.
		are the partially ordered sets of meet-irreducibles and of join-irreducibles, respectively.
		, the partially ordered set of join-irreducibles, and that moreover
	www.math.ucla.edu /~baker/222a/handouts/g_distrib/node6.html (570 words)

	Partially Ordered Sets
		This states that, in any partially ordered set that is not a linear order, there is some pair x,y of elements such that the proportion of linear extensions in which x is above y lies between 1/3 and 2/3.
		A circle order is a partial order that can be represented by discs in the plane, with the order given by containment.
		The dimension of suborders of the Boolean lattice
	www.maths.lse.ac.uk /Personal/graham/research-pos.html (2126 words)

	Examples of Partially Ordered Sets
		is a partial ordering by proving that the properties (1), (2) and (3) above all hold.
		Another example of a partial ordering which arises in the real world is the building of a new house in which there are certain tasks such as digging the foundations, laying the floor, which must be completed before other phases of the construction such as erecting walls and building the roof can be undertaken.
		is called a partially ordered set or poset.
	scom.hud.ac.uk /scomtlm/book/node44.html (306 words)

	ipedia.com: Zorn's lemma Article (Site not responding. Last check: 2007-11-07)
		A subset T is totally ordered if for any s, t in T we have either s ≤ t or t ≤ s.
		This set is partially ordered by set inclusion.
		Since T is totally ordered, we know that J is a subset of K or vice versa.
	www.ipedia.com /zorn_s_lemma.html (827 words)

	Partial Order Scoring (statistics)
		A strict partial order relation is denoted hereafter by «.
		is called a partially ordered set if a strict partial order relation "«" is defined on it.
		In other words, an ordered set is a partially ordered set with additional equivalence relation defined on it, and where the conditions "neither a « b nor b « a" and "a
	www.unesco.org /webworld/idams/Doc/ManualHtml/E2poscor.htm (499 words)

	Physics Help and Math Help - Physics Forums - partially ordered set
		the set of points in a partially ordered set can be represented by its most general and its most specific elements".
		In particular, the elements of a partially ordered set are not necessarily points!
		03-14-2005 09:04 AM I think it's trying to say something like: to keep track of a partially ordered set that has finitely long chains only, then all we need to do is keep track of the ends of all the chains, ie the maxima and minima.
	www.physicsforums.com /printthread.php?t=66914 (351 words)

	PlanetMath: equivalence of Zorn's lemma and the axiom of choice (Site not responding. Last check: 2007-11-07)
		be a proper class, in contradiction to the fact that it is a set.
		There are some stylistic changes that I would make, but these are merely a matter of taste.
		First, there is your f on p"X. Define U:P(X)->P(X) by U(x)={yy is an upper bound for x}; if C is the set of chains in X, then there is a choice function h on U"C. Let x be any member of X and define g:Ord->X by transfinite recursion:
	planetmath.org /encyclopedia/ProofOfZornsLemma.html (333 words)

	Type Hierarchies
		Types are organized into partially ordered sets, called type hierarchies.
		Definition 2.1 A partial order on a set P is a relation
		Definition 2.4 A type hierarchy is a non-empty, countable, bounded complete, partially ordered set.
	www.cs.toronto.edu /~mcosmin/publications/thesis/node11.html (198 words)

	[No title]
		B is a partially ordered set in which every subset has a least upper bound (i* *.e., B is a complete join semilattice).
		A complete lattice is * just a partially* ordered set that is complete and cocomplete as a category; the coli* mit of a functor to a lattice is the join of all of the objects in the image, and dual *ly for the limit.
		In particular, BA is isomorphic to the Boolean algebra* * of finite and cofinite subsets of a countable set.
	www.math.purdue.edu /research/atopology/Hovey-Palmieri/bousfield.txt (8591 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Since the subtasks of a method can be partially ordered, this means that subtasks of different methods can be interleaved in a plan.
		This is needed in order to ensure that for all of the methods used to produce that primitive task, the preconditions are evaluated in the correct state of the world.
		Below, we summarize what those advantages and drawbacks are: Planning for tasks in the order that those tasks will be performed makes it possible to know the current state of the world at each step in its planning process, which makes it possible to incorporate significant reasoning power into the planner’s precondition-evaluation mechanism.
	www.aic.nrl.navy.mil /~aha/papers/Nau-et-al-IJCAI-01.doc (3962 words)

	Partially Ordered Sets
		is called a partially ordered set, or a poset, for short.
		Its length is the number of elements minus one.
		We end this section with a definition of the order complex of a poset, which is the standard translation of combinatorial structures into topology.
	www.uni-bayreuth.de /departments/wirtschaftsmathematik/rambau/Diss/diss_MASTER/node33.html (209 words)

	A MOST FUNDAMENTAL FIXED POINT THEOREM (Site not responding. Last check: 2007-11-07)
		Let f be a mapping from a partially ordered set (P, into itself.
		Also, it is not assumed that every nonempty well ordered subset of P has an upper bound or a least upper bound.
		(a) need not be the supremum of the set of the previous iterates; since no such supremum may even exist.
	www.math.ucdavis.edu /~suh/abian/abian-fpt.html (285 words)

	[No title]
		I believe you're thinking of the Mobius Inversion function mu on a partially ordered set.
		In fact, the USUAL Moebius function is a slight generalization of the special form you have indicated.
		Suppose that we have partially ordered sets A_j, all of which are rooted trees with the root designated as 0, and we consider the weak direct product of the A_j, with only a finite number of the coordinates not 0.
	www.math.niu.edu /~rusin/known-math/98/moebius (432 words)

	No Title (Site not responding. Last check: 2007-11-07)
		Title: The Weak Discrepancy of a Partially Ordered Set
		Abstract: In this talk, we discuss criteria for assigning integer ranks to elements of a partially ordered set.
		As an application, a manager may have a partial order of employees based on their performance and needs to assign an integer (salary level) to each employee.
	www.math.tau.ac.il /~rshamir/Group/meetings/00/Nov_8_1999 (146 words)

Try your search on: Qwika (all wikis)