In
mathematics, a lattice word (or lattice permutation) is a
string
String or strings may refer to:
*String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects
Arts, entertainment, and media Films
* ''Strings'' (1991 film), a Canadian anim ...
composed of positive
integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language ...
s, in which every
prefix
A prefix is an affix which is placed before the stem of a word. Adding it to the beginning of one word changes it into another word. For example, when the prefix ''un-'' is added to the word ''happy'', it creates the word ''unhappy''. Particu ...
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 prefix 12122 contains more 2s than 1s.
See also
*
Dyck word
In the theory of formal languages of computer science, mathematics, and linguistics, a Dyck word is a balanced string of square brackets and The set of Dyck words forms the Dyck language.
Dyck words and language are named after the mathematici ...
References
*
*{{Citation , last1=Macdonald , first1=Ian G. , author1-link=Ian G. Macdonald , title=Symmetric functions and Hall polynomials , edition=Second , series=Oxford Mathematical Monographs , publisher=
The Clarendon Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books ...
and
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...
, year=1995 , isbn=0-19-853489-2 , mr=1354144
Algebraic combinatorics
Combinatorics on words