Lattice word

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In mathematics, a lattice word (or lattice permutation) is a sequence of integers such that in every initial part of the sequence any number i occurs at least as often as the number i + 1. A reverse lattice word, or Yamanouchi word, is a sequence whose reversal is a lattice word. 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.