

A019589


Number of nondecreasing sequences that are differences of two permutations of 1,2,...,n.


0



1, 2, 5, 16, 59, 246, 1105, 5270, 26231, 135036, 713898, 3857113
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OFFSET

1,2


COMMENTS

From Olivier Gérard, Sep 18 2007: (Start)
Number of classes of permutations arrays giving the same partition by the following transformation (equivalent in this case to Xrays but more general): on the matrix representation of a permutation of order n, the sum (i.e., here, number of ones) in the ith antidiagonal is the number of copies of i in the partition.
This gives an injection of permutations of n into partitions with parts at most 2n1. The first or the last antidiagonal can be omitted, reducing the size of parts to 2n2 without changing the number of classes.
This sequence is called Lambda_{n,1} in Louck's paper and appears explicitly on p. 758. Terms up to 10 were computed by Myron Stein (arXiv).
This is similar to the number of Schur functions studied by Di Francesco et al. (A007747) related to the powers of the Vandermonde determinant. Also number of classes of straight (monotonic) crossing bipermutations. (End)


REFERENCES

Olivier Gérard and Karol Penson, Set partitions, multiset permutations and bipermutations, in preparation.
James D. Louck, Power of a determinant with two physical applications, Internat. J. Math. & Math. Sci., Vol. 22, No 4(1999) pp. 745759  S 01611712(99)227457


LINKS

Table of n, a(n) for n=1..12.
C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the xrays of permutations
J.P. Davalan, Permutations et tomographie  Xrays.


CROSSREFS

Sequence in context: A185143 A000753 A007878 * A087949 A028333 A007747
Adjacent sequences: A019586 A019587 A019588 * A019590 A019591 A019592


KEYWORD

nonn,more,nice


AUTHOR

Alex Postnikov (apost(AT)math.mit.edu)


EXTENSIONS

More terms from Olivier Gérard, Sep 18 2007
Two more terms from Vladeta Jovovic, Oct 04 2007


STATUS

approved



