(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 4563, 145]*) (*NotebookOutlinePosition[ 5524, 175]*) (* CellTagsIndexPosition[ 5480, 171]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Documentation for the Tableaux package", "Section"], Cell[TextData[{ "This is some documentation for the ", StyleBox["Mathematica", FontSlant->"Italic"], " package Tableaux. It implements some basic functions related to the \ combinatorial theory of tableaux.\n\nCurrent versions of the package and this \ documentation are available from ", ButtonBox["http://www.math.umn.edu/~drake", ButtonData:>{ URL[ "http://www.math.umn.edu/~drake/"], None}, ButtonStyle->"Hyperlink"], ".\n\n1 December 2004" }], "Text"], Cell["\<\ Since this notebook is all about a certain package, let's begin by \ loading that package.\ \>", "Text"], Cell[BoxData[ \(<< Tableaux`\)], "Input"], Cell["\<\ A tableau is represented by list of lists of integers. A zero \ represents a cell that doesn't yet have a number, and -1 represents a \ nonexistent cell in a skew shape. There are two obviously-named functions \ that will take you from partitions to the corresponding shapes and vice \ versa:\ \>", "Text"], Cell[BoxData[ \(PartitionToFerrersShape[{4, 2, 1, 1}] // TableForm\)], "Input"], Cell[BoxData[ \(PartitionToFerrersShape[{5, 5, 3, 1}, {3, 2, 1}] // TableForm\)], "Input"], Cell["\<\ Here are all semistandard tableaux of shape {4,4,4,1} content \ {4,4,3,1,1}. There are only two, we'll look at the first.\ \>", "Text"], Cell[BoxData[{ \(foo = KostkaSet[{4, 4, 4, 1}, {4, 4, 3, 1, 1}]\), "\[IndentingNewLine]", \(foo[\([1]\)] // TableForm\)}], "Input"], Cell["\<\ This is the n = 5 Kostka matrix. It agrees with MacDonald's book. \ Let's print out the partitions of 5 so you can see how the rows and columns \ are indexed.\ \>", "Text"], Cell[BoxData[{ \(Partitions[5]\), "\[IndentingNewLine]", \(KostkaMatrix[5] // MatrixForm\)}], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Catalog of functions", "Section"], Cell[TextData[{ "Just evaluate the cell below to see the functions available in Tableaux, \ and click on them to see their help blurbs. See the package file for the \ actual definitions of these functions, or use two question marks: ", StyleBox["??PartitionToFerrersShape", FontFamily->"Courier"] }], "Text"], Cell[BoxData[ \(\(?Tableaux`*\)\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Credits, etc", "Section"], Cell[TextData[{ "The Tableaux package and this documentation are by Dan Drake (", ButtonBox["drake@math.umn.edu", ButtonData:>{ URL[ "mailto:drake@math.umn.edu?subject=SymmetricFunctions"], None}, ButtonStyle->"Hyperlink"], ").\n\nThe Tableaux package is \[Copyright] 2004 Dan Drake and may be \ redistributed and/or modified under the terms of the GNU General Public \ License. See Tableaux.m for details." }], "Text"] }, Closed]] }, FrontEndVersion->"5.0 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{661, 877}, WindowMargins->{{Automatic, 231}, {Automatic, 47}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "home", "grad", \ "drake", "research", "op"}, "SymmetricFunctions.nb.ps", CharacterEncoding -> \ "iso8859-1"], "Magnification"->1}, ShowSelection->True ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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