Ultimate Gilbreath Principle Gilbreath shuffle

theorem (the ultimate gilbreath principle)
for permutation π of {1, 2, 3, . . . , n }, following 4 properties equivalent:


π gilbreath permutation.
for each j, top j cards {π(1), π(2), π(3), . . . , π(j)} distinct modulo j.
for each j , k kj ≤ n, j cards { π((k − 1)j + 1), π((k − 1)j +2),. . . , π(kj)} distinct modulo j.
for each j, top j cards consecutive in 1, 2, 3, . . . , n




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