# Overlay alignment

Borrowing triangularArrayLayout from here, I have:

triangularArrayLayout[triArray_List, opts___] :=
Module[{n = Length[triArray]},
Graphics[MapIndexed[
Text[Style[#1,
Large], {Sqrt[3] (n - 1 + #2.{-1, 2}), 3 (n - First[#2] + 1)}/
2] &, triArray, {2}], opts]]

n = 6;
s = 500;
coeffs = triangularArrayLayout[Table[Row[{"C(", i, ",", j, ")"}], {i, 0, n}, {j, 0, i}],
ImageSize -> s];
tri = triangularArrayLayout[Table[Binomial[i, j], {i, 0, n}, {j, 0, i}],
ImageSize -> s];
layers = {Overlay[{coeffs, Show[tri, TextStyle -> GrayLevel[.8]]}, Alignment -> Top],
Overlay[{tri, Show[coeffs, TextStyle -> GrayLevel[.8]]}, Alignment -> Top]};

Manipulate[layers[[u]], {{u, 1, " "}, {1 -> "binomial coefficients",
2 -> "Pascal's triangle"}}, ControlType -> RadioButtonBar]


but the vertical alignment is off:

This is the main issue, but I am also curious how to:

1. typeset the $C(n,r)$ as TraditionalForm (with the varying $n$ and $r$ values throughout)
2. typeset the $C(n,r)$ as $_{n}C_{r}$ (also with the varying $n$ and $r$ values).
-

## 2 Answers

• Using the same option ImagePadding->k in both coeff and tri fixes the vertical alignment problem.
• C is a protected symbol (it is used for representing constants generated in symbolic computations.) Instead you can use \[ScriptCapitalC]:

Then

TraditionalForm[\[ScriptCapitalC][n,r]]


gives

and

 TraditionalForm[\[ScriptCapitalC][9,3]]


gives

• For typsetting C(n,r) as $_{n}C_{r}$

you can use

nCr /: MakeBoxes[nCr[n_, r_], StandardForm] :=
RowBox[{SubscriptBox["\[InvisiblePrefixScriptBase]",  MakeBoxes[n, StandardForm]],
SubscriptBox["C", MakeBoxes[r, StandardForm]]}]


With

 nCr[3, 2]


you get

and

TraditionalForm[nCr[3, 2]]


gives

-
Thanks, this is helpful. – JohnD Dec 5 '12 at 0:18

Version 7 does not have Overlay, but one can produce a similar effect from within Graphics. Using your code with this substitution:

layers = {Graphics[{coeffs[[1]], Opacity[0.3], tri[[1]]}],
Graphics[{tri[[1]], Opacity[0.3], coeffs[[1]]}]};


yields:

-
Thanks, this is also helpful to me. – JohnD Dec 5 '12 at 0:18