  
  
                                  [1XPatternClass[101X
  
  
                          [1XPermutation Pattern Classes[101X
  
  
                                  Version 2.0
  
  
                                  August 2015
  
  
                                 Michael Albert
  
                                  Steve Linton
  
                                 Ruth Hoffmann
  
  
  
  Michael Albert
      Email:    [7Xmailto:malbert at cs.otago.ac.nz[107X
  Steve Linton
      Email:    [7Xmailto:sl4 at st-andrews.ac.uk[107X
  Ruth Hoffmann
      Email:    [7Xmailto:rh347 at icloud.com[107X
  
  -------------------------------------------------------
  [1XAbstract[101X
  [33X[0;0YThe  [10XPatternClass[110X  package  is  build  on the idea of token passing networks
  building  permutation  pattern classes. Those classes are best determined by
  their  basis.  Both sets can be encoded by rank encoding their permutations.
  Each,  the  class  and  its  basis,  in  their encoded form build a rational
  language  [AAR03].  Rational  languages  can  be  easily  computed  by using
  automata,  which  also can be build directly from the token passing networks
  [ALTd.]. Both ways will build the same language, i.e. the same automaton.[133X
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2011 by Michael Albert, Steve Linton and Ruth Hoffmann[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (PatternClass)[101X
  
  1 [33X[0;0YIntroduction[133X
  2 [33X[0;0YToken Passing Networks[133X
    2.1 [33X[0;0YSpecific TPN[133X
      2.1-1 Parstacks
      2.1-2 Seqstacks
      2.1-3 BufferAndStack
  3 [33X[0;0YPermutation Encoding[133X
    3.1 [33X[0;0YEncoding and Decoding[133X
      3.1-1 RankEncoding
      3.1-2 RankDecoding
      3.1-3 SequencesToRatExp
  4 [33X[0;0YFrom Networks to Automata[133X
    4.1 [33X[0;0YFunctions[133X
      4.1-1 GraphToAut
      4.1-2 ConstrainedGraphToAut
  5 [33X[0;0YFrom Automata to Networks[133X
    5.1 [33X[0;0YFunctions[133X
      5.1-1 IsStarClosed
      5.1-2 Is2StarReplaceable
      5.1-3 IsStratified
      5.1-4 IsPossibleGraphAut
  6 [33X[0;0YPattern Classes[133X
    6.1 [33X[0;0YTransducers[133X
      6.1-1 Transducer
      6.1-2 DeletionTransducer
      6.1-3 TransposedTransducer
      6.1-4 InvolvementTransducer
      6.1-5 CombineAutTransducer
    6.2 [33X[0;0YFrom Class to Basis and vice versa[133X
      6.2-1 BasisAutomaton
      6.2-2 ClassAutomaton
      6.2-3 BoundedClassAutomaton
      6.2-4 ClassAutFromBaseEncoding
      6.2-5 ClassAutFromBase
      6.2-6 ExpandAlphabet
    6.3 [33X[0;0YDirect Sum of Regular Classes[133X
      6.3-1 ClassDirectSum
    6.4 [33X[0;0YStatistical Inspections[133X
      6.4-1 Spectrum
      6.4-2 NumberAcceptedWords
      6.4-3 AutStateTransitionMatrix
      6.4-4 AcceptedWords
      6.4-5 AcceptedWordsR
  7 [33X[0;0YSome Permutation Essentials[133X
    7.1 [33X[0;0YComplement[133X
      7.1-1 PermComplement
    7.2 [33X[0;0YRank Encoding[133X
      7.2-1 IsRankEncoding
  8 [33X[0;0YProperties of Permutations[133X
    8.1 [33X[0;0YIntervals in Permutations[133X
      8.1-1 IsInterval
    8.2 [33X[0;0YSimplicity[133X
      8.2-1 IsSimplePerm
    8.3 [33X[0;0YPoint Deletion in Simple Permutations[133X
      8.3-1 OnePointDelete
      8.3-2 TwoPointDelete
      8.3-3 PointDeletion
    8.4 [33X[0;0YBlock-Decomposition[133X
      8.4-1 Inflation
      8.4-2 BlockDecomposition
    8.5 [33X[0;0YPlus-Decomposability[133X
      8.5-1 IsPlusDecomposable
    8.6 [33X[0;0YMinus-Decomposability[133X
      8.6-1 IsMinusDecomposable
    8.7 [33X[0;0YSums of Permutations[133X
      8.7-1 PermDirectSum
      8.7-2 PermSkewSum
  9 [33X[0;0YRegular Languages of Sets of Permutations[133X
    9.1 [33X[0;0YInversions in Permutations[133X
      9.1-1 InversionAut
      9.1-2 InversionAutOfClass
    9.2 [33X[0;0YPlus- and Minus-(In)Decomposablilty[133X
      9.2-1 PlusDecomposableAut
      9.2-2 PlusIndecomposableAut
      9.2-3 MinusDecomposableAut
      9.2-4 MinusIndecomposableAut
    9.3 [33X[0;0YLanguage of all non-simple permutations[133X
      9.3-1 LengthBoundAut
      9.3-2 ShiftAut
      9.3-3 NextGap
      9.3-4 GapAut
      9.3-5 SumAut
      9.3-6 GapSumAut
      9.3-7 NonSimpleAut
    9.4 [33X[0;0YSimplicity[133X
      9.4-1 SimplePermAut
    9.5 [33X[0;0YExceptionality[133X
      9.5-1 IsExceptionalPerm
      9.5-2 ExceptionalBoundedAutomaton
  10 [33X[0;0YMiscellaneous functions[133X
    10.1 [33X[0;0YAutomaton Manipulation[133X
      10.1-1 LoopFreeAut
      10.1-2 LoopVertexFreeAut
  
  
  [32X
