How to dynamically/recursively add columns to generate permutations..

Thanks,

Not very elegant but I managed to get it working by passing previousState and iteration count down the iteration thanks to your push to the right direction.

(N as number, k as number, optional prevStep as any, optional iteration as number) as any =>
let
    decisionslist1 = Table.FromList(List.Generate(()=>[x = 0, y=0],each [x] <= N, each [x=[x]+1,y=Number.Power(2,x-1)],each [y]), Splitter.SplitByNothing(), null, null, ExtraValues.Error),
    iteration = if iteration is null then 1 else iteration,
    prevStep = if prevStep = null then decisionslist1 else prevStep,
    cartesian = Table.AddColumn(decisionslist1, "Custom", each prevStep),
    expanded = Table.ExpandTableColumn(cartesian, "Custom", {"Column1"}, {"Column1.1"}),
    renamed = Table.RenameColumns(expanded,{{"Column1", "a"}, {"Column1.1", "b"}}),
    select = Table.SelectRows(renamed,each ([a] <> [b]) or (Number.From([a]) = 0 and Number.From([b])=0)),
    sum = Table.AddColumn(select, "Column1", each [a]+[b]),
    removeDuplicates = Table.Distinct(sum, {"Column1"}),
    removedcolumns = Table.RemoveColumns(removeDuplicates,{"a", "b"}),
    decisionlist2 = if iteration = k then prevStep else GetPermutations(N,k,removedcolumns, iteration+1),
    out = decisionlist2
in
    out

coupling this with the toBinary function from Solved: Re: Number to Binary - Microsoft Fabric Community I am able to create the binary numbers(states/decisions for my purpose) up to k set bits at an acceptable performance... 

for N=8, k=2...

Column1	toBinary
0	000000000000000000000000
1	000000000000000000000001
2	000000000000000000000010
3	000000000000000000000011
4	000000000000000000000100
5	000000000000000000000101
6	000000000000000000000110
8	000000000000000000001000
9	000000000000000000001001
10	000000000000000000001010
12	000000000000000000001100
16	000000000000000000010000
17	000000000000000000010001
18	000000000000000000010010
20	000000000000000000010100
24	000000000000000000011000
32	000000000000000000100000
33	000000000000000000100001
34	000000000000000000100010
36	000000000000000000100100
40	000000000000000000101000
48	000000000000000000110000

 I would have shared a more generic function if I could, will do maybe one day if I can.