(* Mathematica program to generate the "Illustration of the section model of partitions (2D view)" *)
n = 10; f1 = {};  f2 = {}; x = 1; p = PartitionsP[n]; d = ConstantArray[Null, { n + 1, p}];
For[i = 1, i <= n, i++, 
  r = DeleteCases[Sort@PadRight[Reverse /@ Cases[IntegerPartitions[i], x_ /; Last[x] != 1]], x_ /; x == 0, 2];
  d[[n - i + 1, 1 ;; PartitionsP[i - 1]]] = 1;
  f2 = f2~Join~Table[{{n - i + 1, n - i + 1}, {j, j}} -> Thin, {j, PartitionsP[i - 1]}];
  d[[n + 1, PartitionsP[i]]] = PartitionsP[i];
  AppendTo[f1, {{n - i + 1, n}, {1, PartitionsP[i]}} -> Thick];
  For[j = 1, j <= Length[r],  j++,
   rj = r[[j]]; y = 1; x++;
   For[k = Length[rj], k > 0, k--,
    rjk = rj[[k]]; d[[n - y + 1, x]] = rjk; y = y + rjk;
    AppendTo[f2, {{n - y + 2, n}, {x, x}} -> Thin]]]];
Grid[d, Frame -> {None, None, Join[f2, f1]}] (* Robert Price,May 12 2020 *)