OFFSET
1,2
COMMENTS
A two-dimensional permutation of n is a vector of three permutations, with the first element being the identity permutation. For example, ( (1 2 3) (1 3 2) (3 1 2) ) is a two-dimensional permutation of 3. The example is a simple two-dimensional permutation because none of the intervals of length 2 in the permutations is common among all three. On the other hand, ( (1 2 3) (1 3 2) (2 3 1) ) is not simple because the intervals covering 2 and 3 are common among all three permutations.
LINKS
M. H. Albert, M. D. Atkinson and M. Klazar, The enumeration of simple permutations, Journal of Integer Sequences 6 (2003), Article 03.4.4.
Hao Zhang and Daniel Gildea, Enumeration of Factorizable Multi-Dimensional Permutations, J. Integer Sequences 10 (2007), Article 07.5.8.
CROSSREFS
KEYWORD
nonn
AUTHOR
Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008
STATUS
approved