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Holding arguments of a family of functions


I am building a family of functions, parametrized by 2 variables.
These functions take one argument, so i have these definitions:

f[1,3][y_]:=....
f[1,2][y_]:=....
f[1,3][y_]:=...
f[2,1][y_]:=....

etc. As you see it's a case of subvalues being defined.

The problem is that I also require that the y argument should be held.
That is the functions should have something like

Attributes[f[m,n]]={HoldFirst};

But this is not acceptable to Mathematica, since Attributes only takes
symbols.

Even using

Attributes[f]={HoldAll};

does not seem to work.
So , how can i keep the argument y held?


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