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In mathematics, a lattice word (or lattice permutation) is a string composed of positive integers, in which every prefix contains at least as many positive integers i as integers i + 1.

A reverse lattice word, or Yamanouchi word, is a string whose reversal is a lattice word.

Examples


For instance, 11122121 is a lattice permutation, so 12122111 is a Yamanouchi word, but 12122111 is not a lattice permutation, since the sub-word 12122 contains more two's than one's.

See also


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