A133262 Number of two-dimensional simple permutations.

1, 4, 8, 172, 5204, 222716, 12509188, 889421564, 78097622276, 8312906703868, 1056520142488580, 158263730949406716, 27626236450406776836, 5563092167972597137404, 1280742543230231763615748, 334405228960123174787678204, 98317121153947856929753989124, 32339023133437156084762282819580, 11831483864832785151824395066146820, 4789379698138059405310741712024371196

Offset: 1

Author

Hao Zhang and Daniel Gildea (zhanghao(AT)cs.rochester.edu), Oct 15 2007

Keywords

• nonn

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

Cf. A006318, A111111.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 10 2008