cp's OEIS Frontend

A239068 Triangle read by rows: row n lists the smallest positive ideal non-symmetric multigrade of degree n, or 2n+2 zeros if none.

%I A239068 #4 Mar 10 2014 22:26:59
%S A239068 1,6,9,3,3,10,1,10,12,23,3,5,16,22,1,7,17,26,30,2,5,21,22,31,1,10,18,
%T A239068 35,37,47,2,7,25,26,43,45,1,19,20,51,57,80,82,2,12,31,40,69,71,85,1,8,
%U A239068 24,51,54,82,83,97,2,6,27,43,64,73,89,96
%N A239068 Triangle read by rows: row n lists the smallest positive ideal non-symmetric multigrade of degree n, or 2n+2 zeros if none.
%C A239068 The main entry for this topic is A239066.
%C A239068 A multigrade x1<=x2<=…<=xs; y1<=y2<=…<=ys is "symmetric" if x1+ys = x2+y(s-1) = … = xs+y1 when s is odd, or x1+xs = x2+x(s-1) = … = x(s/2)+x((s/2)+1) = y1+ys = y2+y(s-1) = … = y(s/2)+y((s/2)+1) when s is even. See A239067.
%C A239068 Any ideal multigrade x1,x2;y1,y2 of degree 1 is symmetric, since x1+x2 = y1+y2. Ideal non-symmetric multigrades are known only for degrees 2,3,4,5,6,7. The ones for degrees 5,6,7 are only conjecturally the smallest ones.
%F A239068 a(n^2 + n - 1) = 1 or 0.
%e A239068 1, 6, 9; 3, 3, 10
%e A239068 1, 10, 12, 23; 3, 5, 16, 22
%e A239068 1, 7, 17, 26, 30; 2, 5, 21, 22, 31
%e A239068 1, 10, 18, 35, 37, 47; 2, 7, 25, 26, 43, 45
%e A239068 1, 19, 20, 51, 57, 80, 82; 2, 12, 31, 40, 69, 71, 85
%e A239068 1, 8, 24, 51, 54, 82, 83, 97; 2, 6, 27, 43, 64, 73, 89, 96
%e A239068 1, 6, 9; 3, 3, 10 is an ideal non-symmetric multigrade of degree 2 as 1+10 != 6+3 and 1^1 + 6^1 + 9^1 = 16 = 3^1 + 3^1 + 10^1 and 1^2 + 6^2 + 9^2 = 118 = 3^2 + 3^2 + 10^2.
%Y A239068 Cf. A239066, A239067.
%K A239068 hard,more,nonn,tabf
%O A239068 1,2
%A A239068 _Jonathan Sondow_, Mar 10 2014