trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Record Bounds and the Inverse Bijection

Record maxima control prefixes and the inverse fundamental bijection is injective on distinct letters.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES14
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Bounds from the last record

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The Fundamental Bijection and Fixed AvoidersThe Fundamental Bijection andFixed AvoidersRecord Bounds and the Inverse BijectionRecord Bounds and the InverseBijectionCycles from Record BlocksCycles from Record BlocksAn Extreme Value in the Inverse ImageAn Extreme Value in the InverseImageExclusion of Large Fixed 231-AvoidersExclusion of Large Fixed231-AvoidersLow Entries in the Forced PrefixLow Entries in the ForcedPrefixIncompatible Middle Cycle DataIncompatible Middle Cycle DataA Consecutive Pair Forced by a ReturnA Consecutive Pair Forced by aReturnThe Prefix before One in a 231-AvoiderThe Prefix before One in a231-AvoiderThe Penultimate Record BlockThe Penultimate Record BlockThe Penultimate Value of the Original WordThe Penultimate Value of theOriginal WordThe Initial Pair after the Maximum and OneThe Initial Pair after theMaximum and OneSize Bound for Indecomposable Fixed 312-AvoidersSize Bound for IndecomposableFixed 312-AvoidersThe Entry Following the MaximumThe Entry Following the MaximumAn Upward Edge and a Later Intermediate ValueAn Upward Edge and a LaterIntermediate ValueRecord-Block Characterization of 132-AvoidanceRecord-Block Characterizationof 132-Avoidance
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/FundamentalBijection/ThetaBasicInverse
Repository path
D5/S3/Combinatorics/FundamentalBijection/ThetaBasicInverse.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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