User blog comment:Mh314159/A hopefully powerful new system/@comment-33713741-20190627114835/@comment-39585023-20190627154306

Thank you again. Is this a clearer way to define that function, still using ellipses but explaining what they mean?

drop all zeroes and collapse remaining entries

if y is a string of any length a,b,c,...,q with final entry q, then y' is the same string with the penultimate entry decreased by 1, and

[n][y] = n][y' [[a][y'],[b][y'],[c][y'],...q-1]

And for the examples, I think you missed the q-1 part of the definition, possibly because it wasn't defined clearly enough in the original. Using your formulation, I get the following:

[n][p+1,1] = [n][p,1]p+1][p,1],0] which by the rule of dropping zeroes and collapsing becomes [n][p,1][[p+1][p,1 ​​​​​​and this agrees with the examples.  Notice that the last term in the second set of brackets is not [q][y'] but is simple q-1 (otherwise it doesn't terminate).

Thank you very much, and any further thoughts appreciated.