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We compute the winning probabilities for all pairs of permutations of length 3 and some pairs of length 4, showing that, as in the original version for words, the game is non-transitive. Our proofs introduce new bijections for consecutive patterns in permutations. We also give some formulas to compute the winning probabilities more generally, and conjecture a winning strategy for the second player when $k$ is arbitrary.
From: Sergi Elizalde [view email]
[v1]
Tue, 9 Apr 2024 19:26:25 UTC (23 KB)
[v2]
Wed, 6 Aug 2025 17:59:14 UTC (23 KB)
[v3]
Mon, 27 Apr 2026 21:48:56 UTC (24 KB)
[v4]
Mon, 6 Jul 2026 15:51:11 UTC (30 KB)
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