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Shift operator, left.
12

%I #14 Feb 18 2022 22:28:24

%S 0,1,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,

%T 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0

%N Shift operator, left.

%C Let A129185 = M, then M*V (V a vector), shifts V to the left. Example M*V, V = [1, 2, 3, ...] = [2, 3, 4, ...]. A129184 = right shift operator.

%H Franck Ramaharo, <a href="https://arxiv.org/abs/2002.06672">A bracket polynomial for 2-tangle shadows</a>, arXiv:2002.06672 [math.CO], 2020.

%F As an infinite matrix, all 1's in the superdiagonal and the rest zeros.

%e First few rows of the matrix:

%e 0, 1;

%e 0, 0, 1;

%e 0, 0, 0, 1;

%e 0, 0, 0, 0, 1;

%e ...

%t Table[PadLeft[{1},n,0],{n,20}]//Flatten//Rest (* _Harvey P. Dale_, Jul 11 2020 *)

%Y Cf. A129184, A129186.

%K nonn,tabf,easy,less

%O 1,1

%A _Gary W. Adamson_, Apr 01 2007