Nonnesting

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Contents

• Catalan Root and Lagrange Coefficient Transform
• Separated Value Cuts
• Deletion of the Least Value
• Occurrence Orders in Doubled Words
• Augmented Dyck Weights
• Permutation and Dyck-Path Encoding
• Separation at Descents
• Downstep-Weighted Dyck Enumeration
• Adjacent Downstep Pairs
• Quadratic Equation for Downstep Weights
• Interleaving Along a Step Sequence
• Singleton Components at Ground Level
• Combined Dyck Weights
• Relation Between Weighted Dyck Series
• Hook-Block Decomposition
• Order Around a Maximum
• Increasing-Block Decomposition
• Avoidance by Increasing Blocks
• Reflection of Dyck Paths
• Dyck Shape of a Doubled Word
• Direct Sums and Primitive Words
• Nonnesting Avoidance and Generating Functions
• Enumeration for Four Forbidden Patterns
• First-Block Order
• Counting Increasing-Order Words
• Structure with Increasing First Occurrences
• Insertion into Increasing-Order Avoiders
• A Large Initial Letter
• Ordering after the First Primitive Block
• Classification of Primitive Avoiders
• Positions after Crossing Insertion
• Unique Primitive Increasing Word
• Removing the Doubled Largest Prefix
• Adding the Doubled Largest Prefix
• Patterns under a Largest-Letter Prefix
• Three-Letter Order Restrictions
• Crossing after an Initial Two
• Primitive Two-Prefix Construction
• Avoidance after Two-Prefix Insertion
• Forced Prefix after an Initial Two
• The Tail after an Initial Two
• Recursive Form of Increasing-Order Words
• Enumeration of Nonnesting Permutations Avoiding 1322
• Weighted Terminal Enumeration
• Kernel Recurrence for 1322 Avoidance
• Prefix Partition for 1322 Avoidance
• Unique Terminal Factorization
• Type I Terminal Insertion
• Type II Terminal Insertion
• Nonnesting under Type II Insertion
• Nonnesting under Type I Insertion
• Transfer Between Two Avoidance Classes
• Enumeration for 1233 and 1322
• Enumeration for 1132 and 2213
• Avoidance from Permitted Gaps
• Compositions for a Fixed Dyck Shape
• Necessary Gaps at Ascents