The On-Line Encyclopedia of Integer Sequences (OEIS)

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A133262

Number of two-dimensional simple permutations.
(history; published version)

#7 by Bruno Berselli at Mon May 25 03:58:31 EDT 2015

STATUS

reviewed

approved

#6 by Joerg Arndt at Mon May 25 03:18:24 EDT 2015

STATUS

proposed

reviewed

#5 by Michel Marcus at Sun May 24 11:10:51 EDT 2015

STATUS

editing

proposed

#4 by Michel Marcus at Sun May 24 11:10:47 EDT 2015

REFERENCES

M. H. Albert, M. D. Atkinson and M. Klazar. The enumeration of simple permutations. J. Integer Sequences 6 (2003), 03.4.4.

LINKS

M. H. Albert, M. D. Atkinson and M. Klazar, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Albert/albert.html">The enumeration of simple permutations</a>, Journal of Integer Sequences 6 (2003), Article 03.4.4.

#3 by Michel Marcus at Sun May 24 11:10:03 EDT 2015

LINKS

Hao Zhang and Daniel Gildea, <a href="httphttps://www.cs.rochesteruwaterloo.educa/journals/JIS/~gildeaVOL10/pubsZhang/zhang-gildea-jis07dperm.pdfhtml">Enumeration of Factorizable Multi-Dimensional Permutations</a>, J. Integer Sequences 10 (2007), Article 07.5.8.

STATUS

approved

editing

#2 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

DATA

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

REFERENCES

Hao Zhang and Daniel Gildea. Enumeration of Factorizable Multi-Dimensional Permutations. J. Integer Sequences 10 (20007), 07.5.8.

LINKS

Hao Zhang and Daniel Gildea, <a href="http://www.cs.rochester.edu/~gildea/pubs/zhang-gildea-jis07.pdf">Enumeration of Factorizable Multi-Dimensional Permutations</a>, J. Integer Sequences 10 (2007), Article 07.5.8.

KEYWORD

nonn,new

nonn

EXTENSIONS

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

#1 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

NAME

Number of two-dimensional simple permutations.

DATA

1, 4, 8, 172, 5204, 222716, 12509188, 889421564

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.

REFERENCES

M. H. Albert, M. D. Atkinson and M. Klazar. The enumeration of simple permutations. J. Integer Sequences 6 (2003), 03.4.4.

Hao Zhang and Daniel Gildea. Enumeration of Factorizable Multi-Dimensional Permutations. J. Integer Sequences 10 (20007), 07.5.8.

CROSSREFS

Cf. A006318, A111111.

KEYWORD

nonn,new

AUTHOR

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

STATUS

approved