Lattice word

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 (named after Takahiko Yamanouchi), 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 prefix 12122 contains more 2s than 1s.

See also

• Dyck word

References

• Fulton, William (1997), Young tableaux, London Mathematical Society Student Texts, vol. 35, Cambridge University Press, ISBN 978-0-521-56724-4, MR 1464693
• Macdonald, Ian G. (1995), Symmetric functions and Hall polynomials, Oxford Mathematical Monographs (Second ed.), The Clarendon Press and Oxford University Press, ISBN 0-19-853489-2, MR 1354144