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Topic: Young diagram

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Partition function (number theory)

Modular group

	YOUNG TABLEAUX : Encyclopedia Entry (Site not responding. Last check: 2007-10-23)
		The conjugate partition is 10 = 3 + 2 + 2 + 2 + 1.
		Young diagrams are in one-to-one correspondence with irreducible representations of the symmetric group over the complex numbers.
		Young tableaux can be also used to construct representations of the symmetric group over arbitrary fields and to study their structure.
	www.bibleocean.com /OmniDefinition/Young_tableaux (809 words)

	Young tableau - Wikipedia, the free encyclopedia
		In mathematics, a Young tableau is a combinatorial object useful in representation theory.
		The conjugate partition is 10 = 3 + 2 + 2 + 2 + 1.
		Young diagrams are in one-to-one correspondence with irreducible representations of the symmetric group.
	en.wikipedia.org /wiki/Young_tableau (706 words)

	Young tableau
		Young tableaux were introduced by Alfred Young, a mathematician at Cambridge University in 1900.
		Young diagrams are in one-to-one correspondence with irreducible representations of the symmetric group.
		Young tableaux can be also used to construct the representations of the symmetric group and to study their structure.
	www.xasa.com /wiki/en/wikipedia/y/yo/young_tableau.html (604 words)

	USCA1 Opinion 04-1334
		In June 2001, Young's mother, acting on her own behalf and as executor of Young's estate, brought a civil rights action in district court asserting claims under section 1983, 42 U.S.C. § 1983 (2000), and under state law, against the city, various officials and the two officers.
		Young, moving to assist, emerged from the restaurant with his own weapon drawn and was shot by Solitro and Saraiva.
		A young associate at Scheck's firm was told to draft a memorandum to support a motion seeking relief from the stipulation on grounds of mistake.
	www.ca1.uscourts.gov /cgi-bin/getopn.pl?OPINION=04-1334.01A (3689 words)

	A Rosetta Stone of Matter
		The rosetta.jpg diagram is based on the ideas of A. Young and the "Standard Model" of modern physics.
		Young's model, which he called a Rosetta Stone of Meaning, traces the path from unity (the circle) to multiplicity by going through duality (opposites), trinity (the triangles), and quaternity, the crosses.
		I associated each particle with a location on Young's diagram because that is where it was forced to be.
	www.rahul.net /raithel/AMYoung/rosetta.html (695 words)

	Light I
		Thomas Young recognized that if light behaved like a wave it would be possible to create patterns of constructive and destructive interference using light.
		Young realized that the bright spots on his screen occurred where the difference in the length of the path traveled by the beams of light was an integer multiple of the wavelength of the light.
		The card that Young used in his apparatus was very thin — only about as thick as the wavelength of the light he was using it to divide, so the light did, indeed, bend around the card.
	visionlearning.com /library/module_viewer.php?mid=132&l=&c3= (2027 words)

	Tableaux
		A Young diagram, or Ferrers diagram, is a collection of boxes, or cells, arranged in left--justified rows, with a weakly decreasing number of boxes in each row.
		A Skew diagram or Skew Shape is the diagram obtained by removing a smaller Young diagram from a larger on that contains it.
		A Skew tableau is a filling on a skew diagram obeying the same restrictions on entries.
	www.math.niu.edu /help/math/magmahelp/text1113.html (813 words)

	Future Positive : Welcome
		Although, at first glance, the two diagrams do not appear to correspond, it appears to me that they are attempts to illustrate essentially the same thing (from alternate "perspectives").
		the diagrams appear to be alternate expressions of a common underlying viewpoint.
		Despite Young's and Kuntz's differing orientations, they appear to have achieved essentially the same insight (1° of freedom in plants, 2° of freedom in animals).
	futurepositive.synearth.net /2002/04/19 (2126 words)

	PlanetMath: integer partition
		Partitions are often drawn as Young diagrams which are rectangular arrays of boxes in which
		The dual partition is the partition obtained by reflecting the Young diagram along the main diagonal.
		For example, the Young diagram of the partition dual to the one above is
	www.planetmath.org /encyclopedia/IntegerPartition.html (169 words)

	Tableaux
		A skew diagram or skew shape is the diagram obtained by deleting a smaller Young diagram from inside a larger one.
		The Young diagram is specified by either the sequence of positive integers P which is a partition, or the tableau t.
		For positive integers i and j such that (i, j) is the co-ordinates of a cell lying on the specified Young diagram, a positive integer is returned which is the length of the hook of that cell.
	www.umich.edu /~gpcc/scs/magma/text1174.htm (4898 words)

	Tableaux
		A skew diagram or skew shape is the diagram obtained by deleting a smaller Young diagram from inside a larger one.
		The Young diagram is specified by either the sequence of positive integers P which is a partition, or the tableau t.
		For positive integers i and j such that (i, j) is the co-ordinates of a cell lying on the specified Young diagram, a positive integer is returned which is the length of the hook of that cell.
	www.math.lsu.edu /magma/text1326.htm (4886 words)

	Dan Romik's home page (Site not responding. Last check: 2007-10-23)
		Two amusing formulas in the combinatorics of Young diagrams are the hook formula for the dimension of a Young diagram (the number of Young tableaux corresponding to the diagram), and the fact that the sum of the squares of dimensions of Young diagrams of size n is equal to n!
		In the case where the diagram is smooth and strictly decreasing, the limit point of the hook walk is an absolutely continuous random variable, and by using discrete approximations I compute its density function from the shape of the diagram (partially proving a conjecture of Kerov).
		This correspondence between measures and shapes of diagrams is related to the mysterious "Markov transform" which appears in various probabilistic and analytic contexts.
	www.stat.berkeley.edu /~romik/explanations/hookwalk.html (197 words)

	[No title]
		The Young diagram of weight d is an arrangement of d squares (boxes) associated to a given partition in the obvious way.
		.,.* fil), 3 the (skew) diagram* ~=~ = (fi1 + ff1,.
		This diagram commutes: the commutativity of the first square follows from the naturality of ~, and the commutativity of the second from the compati- bility of a family.
	hopf.math.purdue.edu /Chalupnik/cohsdr.txt (8238 words)

	Springer Online Reference Works
		An alternative purely combinatorial definition has been given by J.R. Stembridge [a7] in terms of shifted (Young) diagrams.
		Young diagram) in that there is an indentation along the diagonal.
		Young tableaux are replaced by marked shifted tableaux which are defined as follows.
	eom.springer.de /s/s130140.htm (405 words)

	[No title] (Site not responding. Last check: 2007-10-23)
		Theorem: The number of standard young tableau corresponding to a particular young diagram = dim of associated irrep denoted by the diagram.
		Sn has the general symmetry elements built from the symmetrizer, antisymmetrizer, and young diagrams.
		Define a general symmetry as: Yl,q=Sl,qAl,q where l = the particular young* diagram, q= the particular numbering of the young diagram, Sl,q= symmetry on the rows, and Al,q=antisymmetry on the columns.
	www.cs.cmu.edu /afs/cs.cmu.edu/user/jcl/www/classnotes/math/group_theory/Sn.txt (103 words)

	Representation Theory and Young Tableaux (Site not responding. Last check: 2007-10-23)
		We shall develop the combinatorics of Young tableaux and see them in action in the algebra of symmetric functions and representations of the symmetric and general linear groups.
		A `Young diagram' is a collection of boxes or cells, arranged in left-justified rows, with a (weakly) decreasing number of boxes in each row.
		A `Young tableau' is a filling that is (1) weakly increasing across each row and (2) strictly increasing down each column.
	www.public.iastate.edu /~driessel/young-tableaux.html (411 words)

	Dan Romik's home page (Site not responding. Last check: 2007-10-23)
		Two amusing formulas in the combinatorics of Young diagrams are the hook formula for the dimension of a Young diagram (the number of Young tableaux corresponding to the diagram), and the fact that the sum of the squares of dimensions of Young diagrams of size n is equal to n!
		In the case where the diagram is smooth and strictly decreasing, the limit point of the hook walk is an absolutely continuous random variable, and by using discrete approximations I compute its density function from the shape of the diagram (partially proving a conjecture of Kerov).
		This correspondence between measures and shapes of diagrams is related to the mysterious "Markov transform" which appears in various probabilistic and analytic contexts.
	www.msri.org /~dromik/explanations/hookwalk.html (197 words)

	[No title]
		A _standard tableau_ consists of a Young diagram will its cells decorated by numbers, from 1 to the total number of cells, so that the numbers increase along each row and column.
		Then decorating a whole Young diagram with n cells requires n passes, but we only need describe the first pass.
		The first pass works as follows: We begin by picking a cell C_1 in the Young diagram at random (i.e., all cells have equal probability).
	www.math.unh.edu /~dvf/532/Hook_Formula (2168 words)

	Amazon.com: A Wizard Abroad: The Fourth Book in the Young Wizards Series: Books: Diane Duane (Site not responding. Last check: 2007-10-23)
		For a 14-year-old young woman she was spending altogether too much time with one young man. Even if Kit was the only other wizard in the neighborhood, and all the two ever did was to practice their wizardry and go on quests.
		For anyone who has enjoyed the Harry Potter novels, the entire "Young Wizards" series is highly recommended (it starts with "So You Want to Be a Wizard.") Be warned, however, that this is definitely a different kind of reading experience, and you may be hooked.
		Unlike several of the later Young Wizards books, in A WIZARD ABROAD only Nita Callahan is a viewpoint character, for the very good reason that her parents are behaving as one might expect good parents of a fourteen-year-old wizard to behave.
	www.amazon.com /Wizard-Abroad-Fourth-Young-Wizards/dp/0152162380 (3044 words)

	Uses
		Gary Young's diagram is based on his own research in measuring electrical frequency changes at different places on the body when oil was placed on the specific points on the feet.
		Young Living Essential Oils can be combined with any healing practice, whether medical, herbal, psychological, spiritual, subtle, homeopathic, etc. At the very least, they connect us with something at the heart of life and nature, and inspire us.
		Gary Young to purify the air of airborne pathogens and neutralize mildew, cigarette smoke, and other odors found in homes, offices and confined areas.
	members.cox.net /younglivinginfo/Uses.htm (4180 words)

	Matches for:
		Among the problems of the first type, the author discusses the properties of the distribution of the normalized cycle length in a random permutation and the limiting shape of a random (with respect to the Plancherel measure) Young diagram.
		This leads to the study of a continuous analog of the notion of Young diagram, and in particular, to a continuous analogue of the hook walk algorithm, which is well known in the combinatorics of finite Young diagrams.
		The boundary of the Young graph and MacDonald polynomials
	www.mathaware.org /bookstore?fn=20&arg1=mmonoseries&item=MMONO-219 (306 words)

	ReadWriteThink: Lesson Plan: Introducing the Venn Diagram in the Kindergarten Classroom
		Introduce the term Venn diagram, and encourage the students to think of ways that the Venn diagram could be used as a tool to sort various items.
		Using the Two-Circle Venn Diagram Interactive, show the students how a Venn diagram can also be used to record the work they did and display the information to share with others.
		Use the Venn diagram in your literature curriculum by asking students to compare and contrast two characters in a story, two books by the same author, two plots, two different authors, or two different illustrators and their styles.
	www.readwritethink.org /lessons/lesson_view.asp?id=378 (2296 words)

	Astronomy HyperText Book: Stellar Clusters (Site not responding. Last check: 2007-10-23)
		CM diagram Young Cluster In this case we see the Main Sequence fully represented.
		CM diagram 10 Million Years Old Now we are seeing the disappearance of the most massive main sequence stars as their main sequence lifetimes is less than 10 million years.
		CM diagram 1 Billion years Old Now we see that all the blue stars have evolved off the main sequence and that some of the Red Giants have evolved to become White Dwarfs.
	zebu.uoregon.edu /textbook/sc.html (330 words)

	[No title]
		There’s no simple exact formula for p(n), though there is a beautiful and complicated one due to Hardy and Ramanujan, and there is a beautiful and simple form for the generating function of this sequence.
		We can represent a partition by a diagram of dots, called a Ferrers diagram, or by a diagram of boxes, called a Young diagram: ____________ o o o o o __________
		These are precisely the partitions whose Young diagram fits inside an A-by-B rectangle.
	www.math.harvard.edu /~propp/192/11-06.doc (1015 words)

	The Nine Planets Glossary
		When used to describe a planetary surface "young" means that the visible features are of relatively recent origin, i.e.
		Young surfaces exhibit few impact craters and are typically varied and complex.
		The surfaces of Earth, Titan and Io are young; the surfaces of Mercury, Callisto and most other solid bodies in our solar system are old.
	www.nineplanets.org /help.html (4842 words)

	Counting Young Tableaux
		We show that formulas of Gessel, for the generating functions for Young standard tableaux of height bounded by k (see [2]), satisfy linear differential equations, with polynomial coefficients, equivalent to P-recurrences conjectured by Favreau, Krob and the first author (see [1]) for the number of bounded height tableaux and pairs of bounded height tableaux.
		Clearly a partition is characterized by its diagram.
		The conjugate of a partition is the partition with diagram
	bergeron.math.uqam.ca /Bessel/bessel.html (612 words)

	[No title]
		In other words a Young diagram of order n is a visualization of a partition of n.
		Fill the cells of a Young diagram of order n with numbers 1,2,...,n in such a manner that numbers increase in rows from left to right and in columns from top to bottom.
		Further we show the important role of Young diagrams and tableaux in representation theory of S_n and discuss the information about elements of S_n that could be obtained from Young tableaux.
	www.math.technion.ac.il /~techm/20021210121020021210mel (156 words)

	Skew Young Diagram Method in Spectral Decomposition of Integrable Lattice Models II: Higher Levels - Kirillov, Kuniba, ...
		Skew Young Diagram Method in Spectral Decomposition of..
		16 The Bethe ansatz and the combinatorics of Young tableaux (context) - Kirillov, Yu - 1986
		1 Polyhedra in a space of diagrams and the canonical basis in..
	citeseer.ist.psu.edu /kirillov98skew.html (580 words)

	[No title]
		Namely, the symmetric power functor is a Schur functor associated to a Young diagram consisting of a single column while the exterior power is that associated to a one rowed diagram.
		Thus it is quite natural to ask for a natural operation which would relate a Schur functor associated to a Young diagram ~ to the one associated to the conjugate diagram e~(ie.
		the diagram whose rows are columns of ~).
	www.math.purdue.edu /research/atopology/Chalupnik/koeks.txt (2989 words)

	Child Passenger Safety Technical Encyclopedia
		For protection and comfort of a newborn or very young infant, the rear-facing restraint should be reclined so that the angle of the back surface is just enough to allow the baby's head to lie back comfortably, but not more than 45° from vertical.
		CR manufacturers are required to provide printed instructions with diagrams for step-by-step installation of their products, positioning the child, and adjusting the system to fit the child.
		Historically, the product gap for young children over 40 lb has been a serious problem, if the child does not have access to a seat with a lap-shoulder belt to use with a belt-positioning booster or cannot use a booster due to immaturity.
	www.new.carseat.org /Technical/tech_update.htm (13460 words)

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