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Topic: Ferrers diagram

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Young tableau

	Young tableau - Wikipedia, the free encyclopedia
		A Young diagram (also called Ferrers diagram) is a way to represent partitions of a number n.
		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.
	en.wikipedia.org /wiki/Young_tableaux (755 words)

	PlanetMath: integer partition
		Sometimes dots are used instead of boxes, and then the obtained picture is called Ferrers diagram.
		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
	planetmath.org /encyclopedia/YoungDiagram.html (169 words)

	Info on Numerical Partitions
		A Ferrers diagram is a pictorial representation of a partition.
		Each row of the diagram corresponds to one part of the partition; a part of size k is expanded into k dots (or squares).
		The idea, in terms of the Ferrers diagram, is to "bend" the distinct odd parts about their middle cell and then stack the bent pieces together.
	www.theory.csc.uvic.ca /~cos/inf/nump/NumPartition.html (594 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 cells in each row.
		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.
	www.umich.edu /~gpcc/scs/magma/text1174.htm (4898 words)

	Future? (Site not responding. Last check: 2007-10-23)
		This image is a diagram showing relations between the various partitions of 9.
		Each arrow indicates that a block in the Ferrers diagram has been legally moved by x units (no number means by 1 unit).
		Each partition is then at a certain 'distance' from the origin - this applies an order to the diagram, although there is some ambivalence between partitions at the same distance.
	www.users.globalnet.co.uk /~perry/maths/future/future.htm (139 words)

	DIMACS Focus on Discrete Probability Seminar (Site not responding. Last check: 2007-10-23)
		Taken together, the estimates lead to an asymptotic description of the random Ferrers diagram, close to the one obtained earlier by Szalay and Tur\'an.
		We show further that both the size of a random conjugacy class and the size of the centraliser for every element >from the class are double exponentially distributed in the limit.
		We prove that a continuous time process that describes the random fluctuations of the diagram boundary from the deterministic approximation converges to a Gaussian (non--Markov) process with continuous sample path.
	dimacs.rutgers.edu /Events/1997/Titles/1997/Pittel.html (247 words)

	[No title]
		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.
		This turns out to be a distributive lattice, and from its poset of join-irreducibles one recovers the original Ferrers diagram of L. Maximal chains in YoungsLattice[L] are in one-to-one correspondence with standard Young tableaux of shape L. Build[YoungsLattice[{5,2,2,1,1}],y52211] Building poset y52211...
	www.haverford.edu /math/cgreene/pd/pd3fund.html (2178 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)

	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)

	All about Partition (Site not responding. Last check: 2007-10-23)
		If you want to boot your operating system from the drive you are about to partition, you will need: A primary partition One or more swap partitions Zero or more primary/logical partitionsThe Ferrers diagram is a pictorial representation of a partition.
		For example, the diagram above illustrates the Ferrers diagram of the partition.
		Euler gave a generating function for using the qA partition is a way of writing an integer n as a sum of positive integers where the order of the addends is not significant, possibly subject to one or more additional constraints.
	partition.topplacenow.com /sitemap.htm (290 words)

	SYMMETRICA-MANUAL -- Operations on partitions
		Partitions are represented graphically using the Ferrers diagram.
		The routine to call it is the standard routine ferrers, which then calls the routine ferrers_partition.
		The row with index 0 is the longest row.
	www.mathe2.uni-bayreuth.de /frib/html2/symman/manual_71.html (353 words)

	Diagramas - matport.com - The Phase Diagram Center (Site not responding. Last check: 2007-10-23)
		UML Diagrams for Chapter 3 of Analysis Patterns
		This site is kept free schematics diagram and service manuals of home and office electronics technicians, advices on the repair, useful reference
		A Ferrers diagram represents partitions as patterns of dots, with the nth row having the same number of dots as the nth term in the
	linkfollow.com /lkfl/diagramas.html (263 words)

	A Random Walk On The Rook Placements On A Ferrers Board (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Abstract: :LetB be a Ferrers board, i.e., the board obtained by removing the Ferrers diagram of a partition from the top right corner of an n n chessboard.
		We consider a Markov chain on the set R of rook placements on B in which you can move from one placement to any other legal placement obtained by switching the columns in which two rooks sit.
	citeseer.ist.psu.edu /317806.html (437 words)

	Citations: a likely shape of the random Ferrers diagram - Pittel (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		Packing Ferrers Shapes - Alon, Bóna, Spencer (1999)
		....properties that are shared by the vast majority of the Ferrers shape of size n and imply that these shapes cannot be packed in an efficient way.
		Pittel, On a likely shape of the random Ferrers diagram, Advances in Applied Mathematics 18 (1997), 432--488.
	citeseer.ist.psu.edu /context/16297/0 (1879 words)

	Citebase - A symmetry theorem on a modified jeu de taquin
		A symmetry theorem on a modified jeu de taquin
		For their bijective proof of the hook-length formula for the number of standard tableaux of a fixed shape Novelli, Pak and Stoyanovskii define a modified jeu de taquin which transforms an arbitrary filling of the Ferrers diagram with 1,2,...,n (tabloid) into a standard tableau.
		Their definition relies on a total order of the cells in the Ferrers diagram induced by a special standard tableau, however, this definition also makes sense for the total order induced by any other standard tableau.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0112263 (137 words)

	Citebase - A bijective proof of the hook-length formula for shifted standard tableaux
		We present a bijective proof of the hook-length formula for shifted standard tableaux of a fixed shape based on a modified jeu de taquin and the ideas of the bijective proof of the hook-length formula for ordinary standard tableaux by Novelli, Pak and Stoyanovskii.
		In their proof Novelli, Pak and Stoyanovskii define a bijection between arbitrary fillings of the Ferrers diagram with the integers 1,2,...,n and pairs of standard tableaux and hook tabloids.
		Unfortunately the construction of the shifted hook tabloid is more complicated in the shifted case.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0112261 (163 words)

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