How to write Pascal's Triangle modulo 2

Question

I am writing a document and would love to write Pascal's triangle modulo 2. That is each binomial coefficient modulo 2, "the remainder" when dividing by 2. I found these links (Pascal) of the code for the normal triangle, and tried to just write manually each node, but I just didn't manage to do it. I want a triangle like:

1
11
101
1111
10001
...

Some help would be really appreciated, thank you very much.

Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. — Community, Dec 16 '21 at 20:06
@Bernard I want the normal triangle but with those nodes instead of the normal: 1,11,121,1331,... — MathematicalMoose, Dec 16 '21 at 20:12
Maybe you can use this approach to arrange the numbers: https://tex.stackexchange.com/a/624483/47927 — Jasper Habicht, Dec 16 '21 at 20:53

score 5 · Answer 1 · answered Dec 16 '21 at 20:52

You can probably simplify the logic a bit but

\documentclass{article}
\def\zz#1#2{%
\ifx\empty#2\else
\ifodd\numexpr#1+#2\relax1\else0\fi
\expandafter\zz\expandafter#2%
\fi}
\def\ptriangle#1#2{%
\ifnum#1=0
\def\lastline{1}%
\else
\edef\lastline{\expandafter\zz\expandafter0\lastline0\empty}%
\fi
\lastline\par
\ifnum#1=#2
\expandafter\zzstop
\fi
\ptriangle{\numexpr#1+1\relax}{#2}%
}
\def\zzstop#1#2#3{}
\begin{document}
\ptriangle{0}{5}
\end{document}

score 5 · Accepted Answer · answered Dec 16 '21 at 21:24

Actually, you can just take any example of pascals triangle that you can find on this site and apply mod(2) on the numbers, For example, taking this approach we can get:

\documentclass[tikz,border=5]{standalone}
\usepgflibrary{fpu}
\begin{document}
\def\N{10}
\tikz[x=0.75cm,y=0.5cm, 
  pascal node/.style={font=\footnotesize}, 
  row node/.style={font=\footnotesize, anchor=west, shift=(180:1)}]
  \path  
    \foreach \n in {0,...,\N} { 
      (-\N/2-1, -\n) node[row node/.try]{Row \n:}
        \foreach \k in {0,...,\n}{
          (-\n/2+\k,-\n) node[pascal node/.try] {%
            \pgfkeys{/pgf/fpu}%
            \pgfmathparse{mod(round(\n!/(\k!*(\n-\k)!)),2)}%
            \pgfmathfloattoint{\pgfmathresult}%
            \pgfmathresult%
          }}};
\end{document}

The single minus zero in the last line is probably the result of a rounding error. I leave it to you to fix it ... =)

How to write Pascal's Triangle modulo 2

2 Answers2