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PatternClass

A permutation pattern class package

2.4.5

30 August 2024

Ruth Hoffmann
Email: rh347@st-andrews.ac.uk
Homepage: https://www.st-andrews.ac.uk/computer-science/people/rh347/
Address:
School of Computer Science,
University of St. Andrews,
North Haugh,
St. Andrews,
Fife,
KY16 9SS,
SCOTLAND

Steve Linton
Email: sl4@st-andrews.ac.uk
Homepage: http://sal.host.cs.st-andrews.ac.uk/
Address:
Steve Linton
School of Computer Science,
University of St. Andrews,
North Haugh,
St. Andrews,
Fife,
KY16 9SS,
SCOTLAND

Michael Albert
Email: malbert@cs.otago.ac.nz
Homepage: https://www.otago.ac.nz/computer-science/people/Michael_Albert.html
Address:
Michael Albert
Department of Computer Science,
University of Otago,
PO Box 56,
DUNEDIN 9054,
New Zealand,

Contents

1 Introduction
2 Token Passing Networks
 2.1 Specific TPN

  2.1-1 Parstacks
  2.1-2 Seqstacks
  2.1-3 BufferAndStack
3 Permutation Encoding
 3.1 Encoding and Decoding

  3.1-1 RankEncoding
  3.1-2 RankDecoding
  3.1-3 SequencesToRatExp
4 From Networks to Automata
 4.1 Functions

  4.1-1 GraphToAut
  4.1-2 ConstrainedGraphToAut
5 From Automata to Networks
 5.1 Functions

  5.1-1 IsStarClosed
  5.1-2 Is2StarReplaceable
  5.1-3 IsStratified
  5.1-4 IsPossibleGraphAut
6 Pattern Classes
 6.1 Transducers

  6.1-1 Transducer
  6.1-2 DeletionTransducer
  6.1-3 TransposedTransducer
  6.1-4 InvolvementTransducer
  6.1-5 CombineAutTransducer
 6.2 From Class to Basis and vice versa

  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 Direct Sum of Regular Classes

  6.3-1 ClassDirectSum
 6.4 Statistical Inspections

  6.4-1 Spectrum
  6.4-2 NumberAcceptedWords
  6.4-3 AutStateTransitionMatrix
  6.4-4 AcceptedWords
  6.4-5 AcceptedWordsR
7 Some Permutation Essentials
 7.1 Complement

  7.1-1 PermComplement
 7.2 Rank Encoding

  7.2-1 IsRankEncoding
8 Properties of Permutations
 8.1 Intervals in Permutations

  8.1-1 IsInterval
 8.2 Simplicity

  8.2-1 IsSimplePerm
 8.3 Point Deletion in Simple Permutations

  8.3-1 OnePointDelete
  8.3-2 TwoPointDelete
  8.3-3 PointDeletion
 8.4 Block-Decomposition

  8.4-1 Inflation
  8.4-2 BlockDecomposition
 8.5 Plus-Decomposability

  8.5-1 IsPlusDecomposable
 8.6 Minus-Decomposability

  8.6-1 IsMinusDecomposable
 8.7 Sums of Permutations

  8.7-1 PermDirectSum
  8.7-2 PermSkewSum
9 Regular Languages of Sets of Permutations
 9.1 Inversions in Permutations

  9.1-1 InversionAut
  9.1-2 InversionAutOfClass
 9.2 Plus- and Minus-(In)Decomposablilty

  9.2-1 PlusDecomposableAut
  9.2-2 PlusIndecomposableAut
  9.2-3 MinusDecomposableAut
  9.2-4 MinusIndecomposableAut
 9.3 Language of all non-simple permutations

  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 Simplicity

  9.4-1 SimplePermAut
 9.5 Exceptionality

  9.5-1 IsExceptionalPerm
  9.5-2 ExceptionalBoundedAutomaton
10 Miscellaneous functions
 10.1 Permutation Inclusion Set

  10.1-1 InbetweenPermAutomaton
  10.1-2 InbetweenPermSet
  10.1-3 IsSubPerm
 10.2 Automaton Manipulation

  10.2-1 LoopFreeAut
  10.2-2 LoopVertexFreeAut
References
Index

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