trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Squarefree Numbers Have No Partition Whose Parts and Multiplicities Agree in Mean

A squarefree number above one has no partition whose parts and whose multiplicities share a mean, because squarefreeness turns the mean condition into a count of distinct parts that exceeds the count of parts unless every multiplicity is one.

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The exclusion holds

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Squarefree Numbers Have No Partition Whose Parts and Multiplicities Agree in MeanSquarefree Numbers Have NoPartition Whose Parts andMultiplicities Agree in Mean
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/SquarefreeMeanPartition
Repository path
D5/S3/Combinatorics/SquarefreeMeanPartition.lean
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sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
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b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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