In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern 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 Word stem, 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'' ...
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
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 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 books ...
, year=1995 , isbn=0-19-853489-2 , mr=1354144
Algebraic combinatorics
Combinatorics on words