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Equinumerosity of Inversion Sequences in Class 152

Abstract

The two pattern-avoidance classes in Class 152 are equinumerous at every length.

Theorem 1.1 (The Class 152 equinumerosity).

Lean statement: D5/S3/Combinatorics/InversionSeq/InversionSeqClass152.result

Proof. Machine-checked in Lean as D5/S3/Combinatorics/InversionSeq/InversionSeqClass152.result (✓ std3). ∎

Resolves. Problems/callan-mansour-inversion-class-152 (proved) by D5/S3/Combinatorics/InversionSeq/InversionSeqClass152.result.

Source. Repository-derived.

Acknowledgement. David Callan, Toufik Mansour (2023). Inversion Sequences Avoiding Quadruple Length-3 Patterns. DOI: 10.5281/zenodo.8399694. URL: https://math.colgate.edu/~integers/x78/x78.pdf.

Commentary.

For every nonnegative n, the number of inversion sequences of length n avoiding 010, 100, 102 and 210 equals the number of inversion sequences of length n avoiding 011, 201 and 210.

References