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A019589 Number of nondecreasing sequences that are differences of two permutations of 1,2,...,n. 2
1, 1, 2, 5, 16, 59, 246, 1105, 5270, 26231, 135036, 713898, 3857113 (list; graph; refs; listen; history; text; internal format)



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 X-rays but more general): on the matrix representation of a permutation of order n, the sum (i.e., here, number of ones) in the i-th 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 2n-1. The first or the last antidiagonal can be omitted, reducing the size of parts to 2n-2 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 bi-permutations. (End)


Olivier Gérard and Karol Penson, Set partitions, multiset permutations and bi-permutations, in preparation.


Table of n, a(n) for n=0..12.

C. Bebeacua, T. Mansour, A. Postnikov and S. Severini, On the X-rays of permutations, arXiv:math/0506334 [math.CO], 2005.

J.-P. Davalan, Permutations et tomographie - X-rays.

James D. Louck, Power of a determinant with two physical applications, Internat. J. Math. & Math. Sci., Vol. 22, No 4(1999) pp. 745-759 - S 0161-1712(99)22745-7


Cf. A290052, A289971.

Sequence in context: A280760 A000753 A007878 * A087949 A028333 A007747

Adjacent sequences:  A019586 A019587 A019588 * A019590 A019591 A019592




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


More terms from Olivier Gérard, Sep 18 2007

Two more terms from Vladeta Jovovic, Oct 04 2007

a(0)=1 prepended by Alois P. Heinz, Jul 24 2017



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Last modified August 18 00:28 EDT 2018. Contains 313817 sequences. (Running on oeis4.)