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A289971 Number of permutations of [n] determined by their antidiagonal sums. 3


%S 1,1,2,4,9,20,49,114,277,665,1608,3875

%N Number of permutations of [n] determined by their antidiagonal sums.

%H C. Bebeacua, T. Mansour, A. Postnikov, S. Severini, <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000886">The number of permutations with the same antidiagonal sums</a>.

%o (Sage)

%o def X_ray(pi):

%o P = Permutation(pi).to_matrix()

%o n = P.nrows()

%o return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k,n)))

%o for k in range(1,2*n))

%o @cached_function

%o def X_rays(n):

%o return sorted(X_ray(pi) for pi in Permutations(n))

%o def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))

%o [[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]

%Y Cf. A019589, A002047, A290279, A290280.

%K nonn,more

%O 0,3

%A _Martin Rubey_, Jul 16 2017

%E a(8)-a(11) from _Alois P. Heinz_, Jul 24 2017

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Last modified February 21 07:18 EST 2018. Contains 299390 sequences. (Running on oeis4.)