PatternMatchings

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Contents

• The catalytic change of variables in Rational[t][[q]]
• Concrete completion decompositions
• The full P13 matching and scan correspondence
• Concrete completion decompositions
• Constructing a matching from every accepted scan
• All-size enumeration of matchings avoiding 132, 213 and 321
• Actual H coefficients and boundary elimination inputs
• The future order of arcs avoiding P13
• Normalized bases and pending openings
• Transporting total orders through queue deletion
• Explicit P13 scalar q-series and minimality
• The actual matching functional equation
• The generating function for matchings avoiding 123, 132 and 213
• Avoiding matchings yield accepted scan words
• Catalan-Fibonacci enumeration above the boundary
• A bijection between avoiding matchings and accepted words
• Decoding accepted action words into perfect matchings
• Perfect matchings and the Catalan-Fibonacci generating function
• Encoding matchings by labeled scan actions
• An ordered scan characterizes pattern avoidance
• Generating functions of accepted suffixes