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OP-6238SolvedProbability

Monotonicity of consecutive-adjacency avoidance in random permutations

TheoremDB P2536 · probability

MSC 60 · Probability theory and stochastic processes

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓
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Problem statement

Let pnp_n be the probability that a uniformly random permutation π\pi of {1,…,n}\{1,\ldots,n\} satisfies ∣πi+1−πi∣≠1|\pi_{i+1}-\pi_i|\ne1 for every ii. Is pn+1>pnp_{n+1}>p_n for every n≥4n\ge4?

Lean 4

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Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Resolved. Not Lean-verified

References
  1. [1]TheoremDB P2536 link

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