cp's OEIS Frontend

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

%I A289971 #20 Aug 30 2021 21:34:37
%S A289971 1,1,2,4,9,20,49,114,277,665,1608,3875
%N A289971 Number of permutations of [n] determined by their antidiagonal sums.
%H A289971 C. Bebeacua, T. Mansour, A. Postnikov, and S. Severini, <a href="https://arxiv.org/abs/math/0506334">On the X-rays of permutations</a>, arXiv:math/0506334 [math.CO], 2005.
%H A289971 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/St000886">The number of permutations with the same antidiagonal sums</a>.
%H A289971 Martin Rubey, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Rubey/rubey5.html">Alternating Sign Matrices Through X-Rays</a>, J. Int. Seq., Vol. 24 (2021), Article 21.6.5.
%t A289971 xray[perm_List] := Module[{P, n = Length[perm]}, P[_, _] = 0; Thread[perm -> Range[n]] /. Rule[i_, j_] :> Set[P[i, j], 1]; Table[Sum[P[i - j + 1, j], {j, Max[1, i - n + 1], Min[i, n]}], {i, 1, 2n - 1}]];
%t A289971 a[n_] := xray /@ Permutations[Range[n]] // Tally // Count[#, {_List, 1}]&;
%t A289971 Do[Print[n, " ", a[n]], {n, 0, 10}] (* _Jean-François Alcover_, Feb 28 2020 *)
%o A289971 (Sage)
%o A289971 def X_ray(pi):
%o A289971     P = Permutation(pi).to_matrix()
%o A289971     n = P.nrows()
%o A289971     return tuple(sum(P[k-1-j][j] for j in range(max(0, k-n), min(k,n)))
%o A289971                  for k in range(1,2*n))
%o A289971 @cached_function
%o A289971 def X_rays(n):
%o A289971     return sorted(X_ray(pi) for pi in Permutations(n))
%o A289971 def statistic(pi): return X_rays(pi.size()).count(X_ray(pi))
%o A289971 [[statistic(pi) for pi in Permutations(n)].count(1) for n in range(7)]
%Y A289971 Cf. A019589, A002047, A290279, A290280.
%K A289971 nonn,more
%O A289971 0,3
%A A289971 _Martin Rubey_, Jul 16 2017
%E A289971 a(8)-a(11) from _Alois P. Heinz_, Jul 24 2017