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Topic: Hasse diagram

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	Hasse diagram - Wikipedia, the free encyclopedia
		Any such diagram (given that the vertices are labeled) uniquely determines a partial order, but there are many possible diagrams for specifying a given order.
		The Hasse diagram of S may then be defined abstractly as the set of all ordered pairs (x, y) such that y covers x, i.e., the Hasse diagram may be identified with the inverse of the cover relation.
		Although Hasse diagrams are simple as well as intuitive tools for dealing with finite posets, it turns out to be rather difficult to draw "good" diagrams.
	en.wikipedia.org /wiki/Hasse_diagram (1023 words)

	SELECTION OF PRIORITY PROPERTIES TO ASSESS ENVIRONMENTAL HAZARD OF PESTICIDES TO SURFICIAL WATERS
		The discrepancy is identified at the bottom of the Hasse diagram that indicates that the mancozeb (h2) and maneb (h3) are equivalent objects with the same properties.
		In line 3 of the Hasse diagram only one pesticide EPTC (e6) of the 6 analyzed for [previous plus captan (b3), diazinon (d0), malathion (h1), parathion (j6), methylparathion (s2)] was found; compounds in line 4 were never analyzed for.
		Hasse diagrams avoid the loss of information that occurs when data are aggregated into a ranking index.
	www.butx.com /halfon/selection_of_priority_properties.htm (5573 words)

	iqexpand.com (Site not responding. Last check: 2007-10-20)
		Using the Hasse diagram to assist, such an analysis results in twenty sequences: 00000000, 00000001, 00000011, 00000101, 00000111, 00001111, 00010001, 00010011, 00010101, 00010111, 00011111...
		Hasse Diagram An HD is a simple data structure.
		The final graph is the Hasse diagram of the lattice.
	hasse_diagram.iqexpand.com (1191 words)

	Abundantia Verborum
		Hasse diagrams are used in mathematics to represent a.o.
		As in Venn diagrams, the 'population' of a node is represented by a gray scale, dark being crowded.
		The general rule is that in a Schematic diagram the inhabitants of node A by definition also inhabit all ancestors of A. Or in other words, the population of a node is a (specific) subclass of the population of its father node.
	wwwling.arts.kuleuven.ac.be /genling/abundant/av332.htm (2933 words)

	Wikinfo \| Hasse diagram
		In mathematics, a Hasse diagram (pronounced HAHS uh) is a simple picture of a finite partially ordered set.
		The Hasse diagram of S may then be defined abstractly as the set of all ordered pairs (x, y) such that y covers x, i.e., the Hasse diagram may be identified with the cover relation.
		For example, if a Hasse diagram was drawn of the poset of all the divisors of a number, partially ordered by divisibility, then the number itself would be at the top of the diagram, the number 1 would be at the bottom, and the smallest (prime) divisors would cover the bottom element.
	www.wikinfo.org /wiki.php?title=Hasse_diagram (257 words)

	Hasse diagrams and n-dimensional space\thanks{set in \LaTeX{}}
		With a few modifications to the rules for drawing Hasse diagrams for divisors we have a set of rules which allow one to draw the projection of n dimensional prisms onto the plane.
		The diagram for the divisors of 30 is in fact a projection of a 3-d cube onto a plane.
		Note that for numbers having less than three distinct prime divisors the diagram will always be a plane, so that for the ordering relation ``divides'' we have a trivial way of finding which numbers generate planar graphs.
	users.libero.it /andy.de_paoli/hassediv.html (1069 words)

	Order theory - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-20)
		The Hasse diagram of such a discrete order is just a collection of labeled points, without any edges between them.
		An instructive exercise is to draw the Hasse diagram for the set of natural numbers that are smaller than or equal to 13, ordered by .
		The visualization of orders with Hasse diagrams has a straightforward generalization: instead of displaying lesser elements below greater ones, the direction of the order can also be depicted by giving directions to the edges of a graph.
	www.sciencedaily.com /encyclopedia/order_theory (4063 words)

	Hasse diagram: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-20)
		The Hasse diagram of S may then be defined abstractly as the set of all ordered pairs (x, Exception Handler: No article summary found.
		the Hasse diagram may be identified with the inverse of the cover relation.
		Although Hasse diagrams are simple as well as intuitive tools for dealing with finite posets (In mathematics, a partially ordered set (or poset for short) is a set equipped with a partial order relation,...)
	www.absoluteastronomy.com /ref/hasse_diagram (2283 words)

	Abundantia Verborum
		In the last part of the previous section 3.3.2 Venn, Hasse and Schematic diagrams we saw that Schematic diagrams are inherently linked to the display threshold mechanism, and we explained how this diagram type behaves with the default threshold settings (which is: threshold on, and set to zero percent).
		What this means, in the context of Schematic diagrams, is that the condition for admitting a node to the diagram is that its weight is strictly higher than 0%.
		, the Hasse diagram counterpart of node "
	wwwling.arts.kuleuven.ac.be /genling/abundant/av333.htm (2493 words)

	Talk:Hasse diagram - Wikipedia, the free encyclopedia
		The vertex "3" is not labelled in the first figure.
		I'd fix it myself, but I don't want to draw an inconsistent style in the diagrams.
		It's an SVG file, so probably was made with something like Inkscape.
	en.wikipedia.org /wiki/Talk:Hasse_diagram (162 words)

	Ivars Peterson's MathTrek -Prized Geometric Logic
		The relationships among the integers in the poset {2, 3, 6, 7, 14, 21, 42} can be expressed symbolically in a special type of diagram known as a Hasse diagram, named for mathematician Helmut Hasse (1898-1979).
		A Hasse diagram consists of dots, which represent the elements of a set; and connecting lines, which represent the relationships among the elements.
		For a poset including the divisors of a given integer, the integer itself would be at the top of the diagram and its prime factors would be at the bottom.
	www.maa.org /mathland/mathtrek_4_2_01.html (731 words)

	Hasse diagrams in LaTeX
		Hasse diagrams illustrate the cover relation of a partial order; they're popular for drawing lattices.
		This is definitely the way to go if you need to typeset Hasse diagrams with latex math annotations.
		Another possibility is to use the graphviz package to layout lattice diagrams automatically.
	osl.iu.edu /~tveldhui/misc/hasse.html (680 words)

	The world's top hasse diagram websites
		In the mathematical area of order theory, a Hasse diagram (pronounced HAHS uh, named after Helmut Hasse (1898 - 1979)) is a simple picture of a finite partially ordered set.
		The set of all 15 partitions of the set { 1, 2, 3, 4 } is partially ordered by "refinement", i.e., a finer partition is "less than" a coarser partition.
		The circumstance that more than one labeling of each of the diagrams is possible reflects the fact that the poset in this example is automorphic -- even in many different ways.
	www.websbiggest.com /wiki-article-tab.cfm/hasse_diagram (1051 words)

	[No title]
		}}{10}} \newlabel{f-ex-hl2}{{1.2}{10}} \@writefile{lof}{\contentsline {figure}{\numberline {1.3}{\ignorespaces Hasse diagram of the spin state propositions which are co-measurable.
		The firefly is not drawn.}}{127}} \newlabel{f-ffiab}{{8.2}{127}} \@writefile{toc}{\contentsline {section}{\numberline {8.1}``Firefly-in-a-box'' and generalized urn models}{127}} \citation{wright} \citation{dvur-pul-svo} \citation{wright} \@writefile{lof}{\contentsline {figure}{\numberline {8.3}{\ignorespaces Greechie diagram of the ``firefly-in-the-box'' model drawn in Figure \ref {f-ffiab}.
		}}{138}} \newlabel{f-mds}{{8.7}{138}} \citation{svozil-93} \citation{svozil-tkadlec} \@writefile{lof}{\contentsline {figure}{\numberline {8.8}{\ignorespaces a) Mealy automaton; b) Hasse diagram of the propositional calculus of a).
	tph.tuwien.ac.at /~svozil/publ/QL.AUX (1766 words)

	[No title]
		Done Once a poset has been "built", its Hasse diagram may be displayed: Diagram[sub4] -Graphics- The coefficents of the rank generating function indicate how many elements are at each rank.
		For general Sn the Hasse diagram is a regular graph of degree n-1.
		If G is a graph with vertex set V, the set of partitions of V whose blocks are G-connected forms a join-sublattice of the full partition lattice on V, called the lattice of contractions of G. We illustrate by constructing this lattice when G is a 5-cycle.
	www.haverford.edu /math/cgreene/pd/pd3fund.html (2178 words)

	[No title]
		From this menu, one can draw the Hasse diagram, and display an appropriate linear model, the ANOVA table, expected mean squares and related factor sets.
		Bug fixes: 28 May 1992 - Before, if you closed the Hasse diagram window and then tried to load a new design file, an error occurred and the new file was not loaded.
		The user may now close the previous Hasse diagram window or leave it for comparison with the new one.
	www.stat.ucla.edu /xlispstat/code/statistics/regression/hasse/hasse (1206 words)

	G3M97 Double Project (Site not responding. Last check: 2007-10-20)
		Having computed all the subgroups of a given group, the final stage is to draw the Hasse diagram describing the group-subgroup relationships.
		The button denoted by "Save" exports the Hasse diagram into a Jpeg picture which is stored in the default directory of the Java Interpreter you are using.
		To see which subgroup corresponds to a number in the diagram, select the number in the drop down list and the subgroup will appear in the output area in the top right.
	www.dilan4.freeserve.co.uk /maths/g3m97/final (1257 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		Create a Hasse Diagram in GAP using the function CreateHasseDiagram which takes a list "l" and a function "le" (less-than-or-equals) which defines a partial order on "l".
		Represent the Hasse Diagram as XML/OpenMath in a browser window using DrawHasse.
		At this point the user is given the opportunity to change the name of the diagram from the default value of "user" and to see the OpenMath representation of the diagram.
	www.illywhacker.net /downloads/GAP-README (300 words)

	Order Relation
		Hasse diagrams defined as follows are such graphs.
		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.
		Example 10: For the relation {< a, a >, < a, b >, < a, c >, < b, b >, < b, c >, < c, c >} on set {a, b,c}, the Hasse diagram has the arcs
	www.cs.odu.edu /~toida/nerzic/content/relation/order/order.html (1120 words)

	The 4-ality model for and (Site not responding. Last check: 2007-10-20)
		are those associated to the three simple roots corresponding to the three ends of the Dynkin diagram, and to the highest root.
		The right hand column gives a representative for each orbit, whose weighted Dynkin diagram can be found on the same line.
		Note that the Hasse diagram is almost a chain, except that there are two triples of nilpotent orbits, permuted by the triality automorphisms.
	www.maths.warwick.ac.uk /~bww/nilpotentseries/node3.html (240 words)

	Integrating fuzzy Hasse diagram with multistrategy learning for student modeling in intelligent tutoring systems (Site not responding. Last check: 2007-10-20)
		In addition to combining the bug library and the overlay strategies, this research also incorporates fuzzy theories, classification tree concepts, Hasse diagrams, and layered structure to develop a nonmonotonic student modeling method.
		The Hasse Diagram can be used to present the dynamic feature and to reason for overcoming the problem of incompleteness.
		As a proof of prototype, this research uses C++ to build a prototype of a Fuzzy Hasse Diagram for testing the functions of dealing with dynamic interaction, incompleteness, ambiguity, and inconsistency.
	digitalcommons.stevens.edu /dissertations/AAI9736464 (360 words)

	Math Trek: Prized Geometric Logic, Science News Online, March 31, 2001 (Site not responding. Last check: 2007-10-20)
		The relationships among the integers in the poset {2, 3, 6, 7, 14, 21, 42} can be expressed symbolically in a special type of diagram known as a Hasse diagram, named for mathematician Helmut Hasse (1898—1979).
		Hasse diagram for a given poset and its corresponding geometric figure.
		Carroll studied posets visualized as complex collections of angular forms known as simplexes.
	www.sciencenews.org /20010331/mathtrek.asp (796 words)

	VEGA 0.5 Quick Reference Manual: Functions in HASSE.M (Site not responding. Last check: 2007-10-20)
		DivisibilityLattice[n] computes the Hasse diagram of the Divisibility lattice of number n.
		DivisibilityLatticeWidth[n] computes the width of the Hasse diagram of the Divisibility lattice of the number n.
		SetPartitionLattice[n] computes the Hasse diagram of the Partition lattice of an n-element set.
	vega.ijp.si /Htmldoc/usages/HASSE.HTM (118 words)

	Mereology
		This need not be true in every model for M: a world with only two items, one of which is P-related to the other but not vice versa, would be a counterexample, though not one that could be illustrated with the sort of geometric diagram used in Figure 1.
		Similarly, one may consider the idea that there is always a mereological sum of two or more parts -- i.e., that for any number of objects there exists a whole that consists exactly of those objects.
		Hasse diagram of mereological theories (from weaker to stronger, going uphill).
	plato.stanford.edu /entries/mereology (9671 words)

	Discrete Mathematics (Site not responding. Last check: 2007-10-20)
		Any finite non empty poset has a minimal element.
		Hasse diagram of N, Hasse diagram of N^2 for the lexicographic ordering.
		Two definitions (no infinite descending chain, and any nonempty subset has a minimal element)
	www.cs.chalmers.se /~coquand/DM/week6.html (118 words)

	A Fast Algorithm for Building the Hasse Diagram of a Galois Lattice (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		A Fast Algorithm for Building the Hasse Diagram of a Galois Lattice (2000)
		As the size of the resulting datasets may grow considerably, it becomes essential to keep the algorithmic complexity of the analysis procedures as low as possible.
		This paper presents an e#cient algorithm that computes the Hasse diagram of a Galois lattice from the lattice ground set, i.e., the set of all concepts.
	citeseer.ist.psu.edu /386091.html (218 words)

	IDA: Applet (Site not responding. Last check: 2007-10-20)
		The positive divisors (bigger than 1) of an integer are pictured in a Hasse diagram as follows: Two divisors b and c are connected by a path going up if b is a divisor of c.
		What are the numbers at the bottom of the diagram?
		For what kind of number does the diagram consist of just one node?
	www.win.tue.nl /ida/demo/c1s1ja.html (82 words)

	Citebase - On Degrees in the Hasse Diagram of the Strong Bruhat Order
		Citebase - On Degrees in the Hasse Diagram of the Strong Bruhat Order
		On Degrees in the Hasse Diagram of the Strong Bruhat Order
		let the \it total degree be its valency in the Hasse diagram of the strong Bruhat order on S
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0505020 (570 words)

	Hasse Diagram And Dynamic Feedback Of (ResearchIndex) (Site not responding. Last check: 2007-10-20)
		Abstract: this paper is that the variety K p,m has associated a Hasse diagram, a certain partially ordered set determined by m, p and q.
		In this diagram the number d(p, m, q) can be identified with the number of totally ordered subsets (Update)
		@misc{ xiaochang-hasse, author = "Linear Systems Xiaochang", title = "Hasse Diagram And Dynamic Feedback Of", url = "citeseer.ist.psu.edu/605145.html" }
	citeseer.ist.psu.edu /605145.html (291 words)

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